This document provides the schedule and agenda for a deep reinforcement learning bootcamp. The bootcamp will cover the mathematical and algorithmic foundations of deep RL through lectures and hands-on labs. Over the course of two days, participants will learn about Markov decision processes, exact solution methods, deep Q-networks, policy gradients, trust region policy optimization, and more from leading researchers in the field. The schedule details the timing of lectures, breaks, and labs to help participants understand core algorithms and implement many of them.
Algorithm Design and Complexity - Course 6Traian Rebedea
This document provides an overview of algorithm design and complexity. It discusses different classes of problems including P vs NP problems. P problems can be solved in polynomial time, while NP problems can be verified in polynomial time but may not be solvable in polynomial time. NP-hard problems are at least as hard as NP problems, and NP-complete problems are NP-hard problems that are also in NP. The document describes techniques for solving difficult problems like backtracking and discusses examples like the n-queens problem.
The document provides a review of units and the metric system. It discusses the advantages of the metric system over the US customary system, including its use of consistent prefixes that are multiples of 10. It also covers converting between units, scientific notation, combined units like those for speed and temperature, and basic algebra review. The document aims to prepare students for material covered in an upcoming science course through this units and math review.
The document provides an overview of concepts from a course on automata, computability, and complexity. It discusses expectations for prerequisites, collaboration policies, and examples of finite automata and the languages they recognize. The key points covered are:
- Finite automata are defined formally as 5-tuples representing states, alphabets, transitions, start states, and accepting states.
- Regular operations on languages, such as union, concatenation, and star are introduced.
- It is shown that the class of languages recognizable by finite automata (regular languages) is closed under all basic set operations on languages, including complement, intersection, union, and the regular operations. Proofs of closure properties use constructions to
Mathematics assignment sample from assignmentsupport.com essay writing services https://writeessayuk.com/
The document proves the product rule for derivatives. It begins by writing the derivative of fg as the limit definition. It then subtracts and adds fg(x) to rewrite this in a form where the limit can be split into two pieces. Taking the limits individually and factoring terms provides the product rule, where the derivative of fg is f'g + fg'.
Mathematical modeling involves converting real-life problems into mathematical terms using appropriate conditions and variables. It allows problems from various domains like physics, economics, and engineering to be studied and solved using mathematical formulas, equations, and techniques. The process of mathematical modeling involves identifying the key parameters of a problem, developing mathematical representations and equations, solving the equations, interpreting the results, and modifying or accepting the model based on how well the results match observations. While mathematical modeling has been successfully applied to many problems, limitations include complex real-world situations being difficult to model accurately and challenges in selecting model parameters.
The document provides notes from a physics class that covered topics including friction, conservation of energy, and kinetic and potential energy. Students calculated coefficients of friction, solved problems involving sliding friction, and performed an experiment launching pennies into the air using a ruler. The class discussed forms of energy, energy transformations, and formulas for gravitational potential energy, kinetic energy, and elastic potential energy. Sample problems were worked through applying these concepts and units.
This document describes Euler's method for numerically approximating solutions to differential equations. Euler's method works by breaking the time interval into discrete steps and using the slope of the direction field at each point to estimate the solution at the next time step. The document provides an example of using Euler's method to solve the initial value problem y'(t) = -2y + 4, y(0) = 1, with time step Δt = 0.2 and number of steps N = 5. It includes a table to fill in with the computed approximations to y(t) at each time step.
390 Guided Projects
Guided Project 31: Cooling coffee
Topics and skills: Derivatives, exponential functions
Imagine pouring a cup of hot coffee and letting it cool at room temperature. How does the temperature of the
coffee decrease in time? How long must you wait until the coffee is cool enough to drink? When should you
add an ounce of cold milk to the coffee to accelerate the cooling as much as possible?
A fairly accurate model to describe the temperature changes in a conducting object is Newton’s Law of
Cooling. Suppose that at time t ≥ 0 an object has a temperature of T(t). The Law of Cooling says that the rate at
which the temperature of the object increases or decreases is given by
( ( ) ) , (1)
dT
k T t A
dt
= − −
where A is the ambient (surrounding) temperature and k > 0 is a constant called the conductivity (which is a
property of the cooling object). Newton’s Law of Cooling assumes that the cooling body has a uniform
temperature throughout its interior. This is not strictly accurate, as a cooling body loses heat through its surface.
1. Explain in words what equation (1) means. Specifically, in terms of T and A, when is 0
dT
dt
> and when is
0
dT
dt
< ? For the case of hot coffee cooling to room temperature, which case do you expect to see?
2. Verify by substitution that the solution to equation (1) subject to the initial condition T(0) = T0 is
0( ) ( ) . (2)
ktT t A T A e−= + −
3. Before graphing the temperature function, use equation (2) to evaluate T(0) and limt→∞ T(t). Are these the
values you expect?
4. Consider the case of a cup of hot coffee cooling with an ambient room temperature of A = 60◦ F and the
initial temperature of the coffee is T0 = 200
◦ F. Use a graphing utility to plot the temperature function for
k = 0.3, 0.2, 0.1, and 0.05. Comment on how the curves change with k. Do larger values of k produce faster
or slower rates of temperature change?
5. For the values of A and T0 in Step 4, estimate the value of k that describes the case in which the coffee
cools to 100 degrees in 10 minutes.
Here is an interesting question. Suppose you want to cool your hot coffee to 100◦ F as quickly as possible.
Suppose also that you have one ounce of cold milk with a temperature of 40◦ F that you can add to the
cooling coffee at any time. When should you add the milk to cool the coffee to 100◦ F as quickly as
possible?
6. We need to make an assumption about the effect of cold milk on the temperature of the coffee. A
reasonable assumption is that when milk is added to coffee, the temperature of the coffee immediately
decreases to the average of the coffee temperature and the milk temperature, where the average is weighted
by the volumes. So if we add 1 ounce of milk with temperature Tm to 8 ounces of coffee with temperature
T, the temperature of the mixture will be
1 8 8
. (3)
1 8 9
m m
new
T T T T
T
⋅ .
Algorithm Design and Complexity - Course 6Traian Rebedea
This document provides an overview of algorithm design and complexity. It discusses different classes of problems including P vs NP problems. P problems can be solved in polynomial time, while NP problems can be verified in polynomial time but may not be solvable in polynomial time. NP-hard problems are at least as hard as NP problems, and NP-complete problems are NP-hard problems that are also in NP. The document describes techniques for solving difficult problems like backtracking and discusses examples like the n-queens problem.
The document provides a review of units and the metric system. It discusses the advantages of the metric system over the US customary system, including its use of consistent prefixes that are multiples of 10. It also covers converting between units, scientific notation, combined units like those for speed and temperature, and basic algebra review. The document aims to prepare students for material covered in an upcoming science course through this units and math review.
The document provides an overview of concepts from a course on automata, computability, and complexity. It discusses expectations for prerequisites, collaboration policies, and examples of finite automata and the languages they recognize. The key points covered are:
- Finite automata are defined formally as 5-tuples representing states, alphabets, transitions, start states, and accepting states.
- Regular operations on languages, such as union, concatenation, and star are introduced.
- It is shown that the class of languages recognizable by finite automata (regular languages) is closed under all basic set operations on languages, including complement, intersection, union, and the regular operations. Proofs of closure properties use constructions to
Mathematics assignment sample from assignmentsupport.com essay writing services https://writeessayuk.com/
The document proves the product rule for derivatives. It begins by writing the derivative of fg as the limit definition. It then subtracts and adds fg(x) to rewrite this in a form where the limit can be split into two pieces. Taking the limits individually and factoring terms provides the product rule, where the derivative of fg is f'g + fg'.
Mathematical modeling involves converting real-life problems into mathematical terms using appropriate conditions and variables. It allows problems from various domains like physics, economics, and engineering to be studied and solved using mathematical formulas, equations, and techniques. The process of mathematical modeling involves identifying the key parameters of a problem, developing mathematical representations and equations, solving the equations, interpreting the results, and modifying or accepting the model based on how well the results match observations. While mathematical modeling has been successfully applied to many problems, limitations include complex real-world situations being difficult to model accurately and challenges in selecting model parameters.
The document provides notes from a physics class that covered topics including friction, conservation of energy, and kinetic and potential energy. Students calculated coefficients of friction, solved problems involving sliding friction, and performed an experiment launching pennies into the air using a ruler. The class discussed forms of energy, energy transformations, and formulas for gravitational potential energy, kinetic energy, and elastic potential energy. Sample problems were worked through applying these concepts and units.
This document describes Euler's method for numerically approximating solutions to differential equations. Euler's method works by breaking the time interval into discrete steps and using the slope of the direction field at each point to estimate the solution at the next time step. The document provides an example of using Euler's method to solve the initial value problem y'(t) = -2y + 4, y(0) = 1, with time step Δt = 0.2 and number of steps N = 5. It includes a table to fill in with the computed approximations to y(t) at each time step.
390 Guided Projects
Guided Project 31: Cooling coffee
Topics and skills: Derivatives, exponential functions
Imagine pouring a cup of hot coffee and letting it cool at room temperature. How does the temperature of the
coffee decrease in time? How long must you wait until the coffee is cool enough to drink? When should you
add an ounce of cold milk to the coffee to accelerate the cooling as much as possible?
A fairly accurate model to describe the temperature changes in a conducting object is Newton’s Law of
Cooling. Suppose that at time t ≥ 0 an object has a temperature of T(t). The Law of Cooling says that the rate at
which the temperature of the object increases or decreases is given by
( ( ) ) , (1)
dT
k T t A
dt
= − −
where A is the ambient (surrounding) temperature and k > 0 is a constant called the conductivity (which is a
property of the cooling object). Newton’s Law of Cooling assumes that the cooling body has a uniform
temperature throughout its interior. This is not strictly accurate, as a cooling body loses heat through its surface.
1. Explain in words what equation (1) means. Specifically, in terms of T and A, when is 0
dT
dt
> and when is
0
dT
dt
< ? For the case of hot coffee cooling to room temperature, which case do you expect to see?
2. Verify by substitution that the solution to equation (1) subject to the initial condition T(0) = T0 is
0( ) ( ) . (2)
ktT t A T A e−= + −
3. Before graphing the temperature function, use equation (2) to evaluate T(0) and limt→∞ T(t). Are these the
values you expect?
4. Consider the case of a cup of hot coffee cooling with an ambient room temperature of A = 60◦ F and the
initial temperature of the coffee is T0 = 200
◦ F. Use a graphing utility to plot the temperature function for
k = 0.3, 0.2, 0.1, and 0.05. Comment on how the curves change with k. Do larger values of k produce faster
or slower rates of temperature change?
5. For the values of A and T0 in Step 4, estimate the value of k that describes the case in which the coffee
cools to 100 degrees in 10 minutes.
Here is an interesting question. Suppose you want to cool your hot coffee to 100◦ F as quickly as possible.
Suppose also that you have one ounce of cold milk with a temperature of 40◦ F that you can add to the
cooling coffee at any time. When should you add the milk to cool the coffee to 100◦ F as quickly as
possible?
6. We need to make an assumption about the effect of cold milk on the temperature of the coffee. A
reasonable assumption is that when milk is added to coffee, the temperature of the coffee immediately
decreases to the average of the coffee temperature and the milk temperature, where the average is weighted
by the volumes. So if we add 1 ounce of milk with temperature Tm to 8 ounces of coffee with temperature
T, the temperature of the mixture will be
1 8 8
. (3)
1 8 9
m m
new
T T T T
T
⋅ .
This document contains slides from a lecture on linear programming. It introduces linear programming and how to formulate an optimization model. This includes defining decision variables, constraints, and the objective function. It then demonstrates solving a linear programming problem graphically and in a spreadsheet for an example involving production planning at a tool company. The optimal solution is found to occur at the intersection of two binding constraints. Key steps in linear programming are summarized.
Skiena algorithm 2007 lecture21 other reductionzukun
This document discusses reductions and NP-completeness. It summarizes how reductions can be used to prove that one problem is at least as hard as another by translating instances of one problem into instances of the other. It then gives examples of reductions between several problems like vertex cover, integer partition, satisfiability, and integer programming to prove them NP-complete.
This document outlines the key aspects of the CS 332: Algorithms course. It introduces the purpose of the course as a rigorous introduction to algorithm design and analysis. It provides details on the textbook, instructor, teaching assistant, and covers topics that will be discussed like proof by induction and asymptotic notation. The course aims to teach students how to formally analyze the time and space complexity of algorithms as the problem size increases.
Okay, let me break this down step-by-step:
* Spring constant (k) = 280 N/m
* Mass (m) = 0.0025 kg
* Deflection (x) = 0.03 m
* EPE = 0.5kx2 = 0.5 * 280 N/m * (0.03 m)2 = 0.81 J
* EPE converts to KE on release: KE = 0.81 J = 0.5mv2
* Solve for v: v = √(2 * 0.81 J / 0.0025 kg) = 4 m/s
* Use v to find maximum height using: h = v2/2g = (
Okay, let me break this down step-by-step:
* Spring constant (k) = 280 N/m
* Mass (m) = 0.0025 kg
* Deflection (x) = 0.03 m
* EPE = 0.5kx2 = 0.5 * 280 N/m * (0.03 m)2 = 0.81 J
* EPE converts to KE on release: KE = 0.81 J = 0.5mv2
* Solve for v: v = √(2 * 0.81 J / 0.0025 kg) = 4 m/s
* Use v to find maximum height using: h = v2/2g = (
Okay, let's break this down step-by-step:
* EPE = 0.5 * k * x^2
= 0.5 * 280 N/m * (0.03 m)^2
= 0.42 J
* EPE converts to KE at the top of the trajectory
* KE = 0.5 * m * v^2
= 0.5 * 0.0025 kg * v^2
= 0.42 J
* Solve for v:
0.42 J = 0.5 * 0.0025 kg * v^2
v = √(0.42 J / 0.5 * 0.0025 kg)
= √16.8
=
This document provides information about a physics coaching class on thermal expansion including:
1) An outline of topics to be covered such as heat, temperature, gas laws, thermodynamics, and numerical problems.
2) Formulas and explanations for linear expansion, volumetric expansion, and proving the relationship between the coefficients.
3) Sample problems demonstrating calculations of changes in length and volume for various materials when temperatures change.
4) Past physics exam problems on thermal expansion and their step-by-step solutions.
5) Key concepts about heat, temperature, different temperature scales, and definitions of related thermal quantities like specific heat.
In summary, the document outlines a physics coaching course on thermal
This document describes the CSE 215 Algorithms course. It provides an overview of the course purpose, textbook, instructor, grading policy, prerequisites, and topics to be covered including proof by induction, asymptotic notation, and analysis of algorithms. The analysis will focus on determining the asymptotic performance of algorithms as the problem size increases. Proof techniques like induction will be used to analyze algorithms precisely.
Problem statement:
Given an array of numbers
A=[x0,x1,...x(N-1)]
Calculate the sum S(A) using recursion.
Here I am deriving the steps and providing Algorithm
This document contains examples and solutions for exercises involving recursive definitions and structural induction. It defines recursive functions such as the sum of integers, maximum/minimum values, bit string parsing, and Ackermann's function. Proofs by structural induction are provided to show properties of the recursively defined sets and functions.
The document compares several nonlinear and linear stabilization schemes (SUPG, dCG91, Entropy Viscosity) for solving advection-diffusion equations using finite element methods. It presents results of applying the different schemes to stationary and non-stationary test equations, comparing maximum overshoot and undershoot, smearing, and convergence orders. For both linear and quadratic elements, the nonlinear dCG91 and Entropy Viscosity schemes showed smaller overshoots and undershoots than linear schemes like SUPG and no stabilization.
Mid semexam | Theory of Computation | Akash Anand | MTH 401A | IIT KanpurVivekananda Samiti
This document contains the details of an exam for an undergraduate course on the theory of computation. The exam consists of 5 questions testing students' knowledge of formal languages and automata. Question 1 has 5 true/false statements to verify about language properties. Question 2 defines string reversal and proves an identity. Question 3 proves a language of prime-length strings is not regular. Question 4 minimizes a finite state machine. Question 5 involves writing a context-free grammar and pushdown automaton for a specified language.
This lecture discusses model-free prediction methods for estimating the value function of an unknown Markov decision process (MDP) from experience without a model of the MDP dynamics. Monte-Carlo (MC) methods learn directly from complete episodes without bootstrapping, while temporal-difference (TD) methods learn online by bootstrapping from incomplete episodes. TD(λ) combines the advantages of MC and TD methods by using eligibility traces to incorporate information from future time steps into the current update.
This document discusses various regularization techniques for deep learning models. It defines regularization as any modification to a learning algorithm intended to reduce generalization error without affecting training error. It then describes several specific regularization methods, including weight decay, norm penalties, dataset augmentation, early stopping, dropout, adversarial training, and tangent propagation. The goal of regularization is to reduce overfitting and improve generalizability of deep learning models.
This lecture covers planning by dynamic programming. It introduces dynamic programming and its requirements of optimal substructure and overlapping subproblems. It then discusses policy evaluation, policy iteration, and value iteration as the main dynamic programming algorithms. Policy evaluation evaluates a given policy through iterative application of the Bellman expectation equation. Policy iteration alternates between policy evaluation and policy improvement by acting greedily with respect to the value function. Value iteration directly applies the Bellman optimality equation through iterative backups. The lecture also discusses extensions such as asynchronous dynamic programming and prioritized sweeping.
This document provides an overview of deep feedforward networks. It begins with an example of using a network to solve the XOR problem. It then discusses gradient-based learning and backpropagation. Hidden units with rectified linear activations are commonly used. Deeper networks can more efficiently represent functions and generalize better than shallow networks. Architecture design considerations include width, depth, and number of hidden layers. Backpropagation efficiently computes gradients using the chain rule and dynamic programming.
This document provides a summary of Lecture 2 on Markov Decision Processes. It begins with an introduction to Markov processes and their properties. Markov decision processes are then introduced as Markov processes where decisions can be made. The key components of MDPs are defined, including states, actions, transition probabilities, rewards and policies. Value functions are also introduced, which estimate the long-term value or return of states and state-action pairs. Examples are provided throughout to illustrate these concepts.
The document discusses numerical concerns for implementing deep learning algorithms. It covers topics like:
1) Algorithms specified with real numbers but implemented with finite bits can lead to rounding errors and instability.
2) Gradient descent, curvature, and saddle points which are important for iterative optimization.
3) Conditioning problems can cause gradient descent to be slow and fail to exploit curvature. Learning rates must account for curvature.
The document discusses attention models for sequence to sequence learning. It introduces attention mechanisms that allow a model to focus on specific parts of the input sequence when generating each token of the output sequence. Examples are given of attention models for neural machine translation and image caption generation, including the computation of attention weights and visualization of attention maps.
This document provides an overview of an introductory lecture on reinforcement learning. The key points covered include:
- Reinforcement learning involves an agent learning through trial-and-error interactions with an environment by receiving rewards.
- The goal of reinforcement learning is for the agent to select actions that maximize total rewards. This involves making decisions to balance short-term versus long-term rewards.
- Major components of a reinforcement learning agent include its policy, which determines its behavior, its value function which predicts future rewards, and its model which represents its understanding of the environment's dynamics.
Stochastic computation graphs provide a framework for automatically deriving unbiased gradient estimators. They generalize backpropagation to deal with random variables by treating the computation graph as a DAG with both deterministic and stochastic nodes. This allows gradients to be computed through expectations, enabling techniques like policy gradients for reinforcement learning and variational inference. The document describes several policy gradient methods that use stochastic computation graphs to compute gradients, including SVG(0), SVG(1), and DDPG. These methods have been successfully applied to robotics tasks and driving.
This document contains slides from a lecture on linear programming. It introduces linear programming and how to formulate an optimization model. This includes defining decision variables, constraints, and the objective function. It then demonstrates solving a linear programming problem graphically and in a spreadsheet for an example involving production planning at a tool company. The optimal solution is found to occur at the intersection of two binding constraints. Key steps in linear programming are summarized.
Skiena algorithm 2007 lecture21 other reductionzukun
This document discusses reductions and NP-completeness. It summarizes how reductions can be used to prove that one problem is at least as hard as another by translating instances of one problem into instances of the other. It then gives examples of reductions between several problems like vertex cover, integer partition, satisfiability, and integer programming to prove them NP-complete.
This document outlines the key aspects of the CS 332: Algorithms course. It introduces the purpose of the course as a rigorous introduction to algorithm design and analysis. It provides details on the textbook, instructor, teaching assistant, and covers topics that will be discussed like proof by induction and asymptotic notation. The course aims to teach students how to formally analyze the time and space complexity of algorithms as the problem size increases.
Okay, let me break this down step-by-step:
* Spring constant (k) = 280 N/m
* Mass (m) = 0.0025 kg
* Deflection (x) = 0.03 m
* EPE = 0.5kx2 = 0.5 * 280 N/m * (0.03 m)2 = 0.81 J
* EPE converts to KE on release: KE = 0.81 J = 0.5mv2
* Solve for v: v = √(2 * 0.81 J / 0.0025 kg) = 4 m/s
* Use v to find maximum height using: h = v2/2g = (
Okay, let me break this down step-by-step:
* Spring constant (k) = 280 N/m
* Mass (m) = 0.0025 kg
* Deflection (x) = 0.03 m
* EPE = 0.5kx2 = 0.5 * 280 N/m * (0.03 m)2 = 0.81 J
* EPE converts to KE on release: KE = 0.81 J = 0.5mv2
* Solve for v: v = √(2 * 0.81 J / 0.0025 kg) = 4 m/s
* Use v to find maximum height using: h = v2/2g = (
Okay, let's break this down step-by-step:
* EPE = 0.5 * k * x^2
= 0.5 * 280 N/m * (0.03 m)^2
= 0.42 J
* EPE converts to KE at the top of the trajectory
* KE = 0.5 * m * v^2
= 0.5 * 0.0025 kg * v^2
= 0.42 J
* Solve for v:
0.42 J = 0.5 * 0.0025 kg * v^2
v = √(0.42 J / 0.5 * 0.0025 kg)
= √16.8
=
This document provides information about a physics coaching class on thermal expansion including:
1) An outline of topics to be covered such as heat, temperature, gas laws, thermodynamics, and numerical problems.
2) Formulas and explanations for linear expansion, volumetric expansion, and proving the relationship between the coefficients.
3) Sample problems demonstrating calculations of changes in length and volume for various materials when temperatures change.
4) Past physics exam problems on thermal expansion and their step-by-step solutions.
5) Key concepts about heat, temperature, different temperature scales, and definitions of related thermal quantities like specific heat.
In summary, the document outlines a physics coaching course on thermal
This document describes the CSE 215 Algorithms course. It provides an overview of the course purpose, textbook, instructor, grading policy, prerequisites, and topics to be covered including proof by induction, asymptotic notation, and analysis of algorithms. The analysis will focus on determining the asymptotic performance of algorithms as the problem size increases. Proof techniques like induction will be used to analyze algorithms precisely.
Problem statement:
Given an array of numbers
A=[x0,x1,...x(N-1)]
Calculate the sum S(A) using recursion.
Here I am deriving the steps and providing Algorithm
This document contains examples and solutions for exercises involving recursive definitions and structural induction. It defines recursive functions such as the sum of integers, maximum/minimum values, bit string parsing, and Ackermann's function. Proofs by structural induction are provided to show properties of the recursively defined sets and functions.
The document compares several nonlinear and linear stabilization schemes (SUPG, dCG91, Entropy Viscosity) for solving advection-diffusion equations using finite element methods. It presents results of applying the different schemes to stationary and non-stationary test equations, comparing maximum overshoot and undershoot, smearing, and convergence orders. For both linear and quadratic elements, the nonlinear dCG91 and Entropy Viscosity schemes showed smaller overshoots and undershoots than linear schemes like SUPG and no stabilization.
Mid semexam | Theory of Computation | Akash Anand | MTH 401A | IIT KanpurVivekananda Samiti
This document contains the details of an exam for an undergraduate course on the theory of computation. The exam consists of 5 questions testing students' knowledge of formal languages and automata. Question 1 has 5 true/false statements to verify about language properties. Question 2 defines string reversal and proves an identity. Question 3 proves a language of prime-length strings is not regular. Question 4 minimizes a finite state machine. Question 5 involves writing a context-free grammar and pushdown automaton for a specified language.
This lecture discusses model-free prediction methods for estimating the value function of an unknown Markov decision process (MDP) from experience without a model of the MDP dynamics. Monte-Carlo (MC) methods learn directly from complete episodes without bootstrapping, while temporal-difference (TD) methods learn online by bootstrapping from incomplete episodes. TD(λ) combines the advantages of MC and TD methods by using eligibility traces to incorporate information from future time steps into the current update.
This document discusses various regularization techniques for deep learning models. It defines regularization as any modification to a learning algorithm intended to reduce generalization error without affecting training error. It then describes several specific regularization methods, including weight decay, norm penalties, dataset augmentation, early stopping, dropout, adversarial training, and tangent propagation. The goal of regularization is to reduce overfitting and improve generalizability of deep learning models.
This lecture covers planning by dynamic programming. It introduces dynamic programming and its requirements of optimal substructure and overlapping subproblems. It then discusses policy evaluation, policy iteration, and value iteration as the main dynamic programming algorithms. Policy evaluation evaluates a given policy through iterative application of the Bellman expectation equation. Policy iteration alternates between policy evaluation and policy improvement by acting greedily with respect to the value function. Value iteration directly applies the Bellman optimality equation through iterative backups. The lecture also discusses extensions such as asynchronous dynamic programming and prioritized sweeping.
This document provides an overview of deep feedforward networks. It begins with an example of using a network to solve the XOR problem. It then discusses gradient-based learning and backpropagation. Hidden units with rectified linear activations are commonly used. Deeper networks can more efficiently represent functions and generalize better than shallow networks. Architecture design considerations include width, depth, and number of hidden layers. Backpropagation efficiently computes gradients using the chain rule and dynamic programming.
This document provides a summary of Lecture 2 on Markov Decision Processes. It begins with an introduction to Markov processes and their properties. Markov decision processes are then introduced as Markov processes where decisions can be made. The key components of MDPs are defined, including states, actions, transition probabilities, rewards and policies. Value functions are also introduced, which estimate the long-term value or return of states and state-action pairs. Examples are provided throughout to illustrate these concepts.
The document discusses numerical concerns for implementing deep learning algorithms. It covers topics like:
1) Algorithms specified with real numbers but implemented with finite bits can lead to rounding errors and instability.
2) Gradient descent, curvature, and saddle points which are important for iterative optimization.
3) Conditioning problems can cause gradient descent to be slow and fail to exploit curvature. Learning rates must account for curvature.
The document discusses attention models for sequence to sequence learning. It introduces attention mechanisms that allow a model to focus on specific parts of the input sequence when generating each token of the output sequence. Examples are given of attention models for neural machine translation and image caption generation, including the computation of attention weights and visualization of attention maps.
This document provides an overview of an introductory lecture on reinforcement learning. The key points covered include:
- Reinforcement learning involves an agent learning through trial-and-error interactions with an environment by receiving rewards.
- The goal of reinforcement learning is for the agent to select actions that maximize total rewards. This involves making decisions to balance short-term versus long-term rewards.
- Major components of a reinforcement learning agent include its policy, which determines its behavior, its value function which predicts future rewards, and its model which represents its understanding of the environment's dynamics.
Stochastic computation graphs provide a framework for automatically deriving unbiased gradient estimators. They generalize backpropagation to deal with random variables by treating the computation graph as a DAG with both deterministic and stochastic nodes. This allows gradients to be computed through expectations, enabling techniques like policy gradients for reinforcement learning and variational inference. The document describes several policy gradient methods that use stochastic computation graphs to compute gradients, including SVG(0), SVG(1), and DDPG. These methods have been successfully applied to robotics tasks and driving.
The document summarizes several advanced policy gradient methods for reinforcement learning, including trust region policy optimization (TRPO), proximal policy optimization (PPO), and using the natural policy gradient with the Kronecker-factored approximation (K-FAC). TRPO frames policy optimization as solving a constrained optimization problem to limit policy updates, while PPO uses a clipped objective function as a pessimistic bound. Both methods improve upon vanilla policy gradients. K-FAC provides an efficient way to approximate the natural policy gradient using the Fisher information matrix. The document reviews the theory and algorithms behind these methods.
1) When approaching new problems, start with small test problems and use visualization to interpret the learning process. Make early tasks easier by providing better features or shaping rewards.
2) Ongoing development requires continual benchmarking, using multiple random seeds, and automating experiments. Key parameters like discount factor and action frequency require tuning.
3) For policy gradient strategies, monitor policy entropy and KL divergence as diagnostics. Use baseline explained variance and initialize policies for maximum entropy.
This document summarizes a deep reinforcement learning approach to train a neural network policy for the game of Pong. The policy network maps game screen images to action probabilities. Policy gradients are used to optimize the network by collecting rollouts of the current policy and using reward signals to increase the probability of actions that led to higher rewards. The network is trained by running many iterations of collecting rollouts, calculating policy gradients with advantage weighting, and updating the network parameters to reinforce successful actions.
This document contains slides about policy gradients, an approach to reinforcement learning. It discusses the likelihood ratio policy gradient method, which estimates the gradient of expected return with respect to the policy parameters. The gradient aims to increase the probability of high-reward paths and decrease low-reward paths. The derivation from importance sampling is shown, and it is noted that this suggests looking at more than just the gradient. Fixes for practical use include adding a baseline to reduce variance and exploiting temporal structure in the paths.
This document summarizes Deep Q-Networks (DQN), a deep reinforcement learning algorithm that was able to achieve human-level performance on many Atari 2600 games. The key ideas of DQN include using a deep neural network to approximate the Q-function, experience replay to increase data efficiency, and a separate target network to stabilize learning. DQN has inspired many follow up algorithms, including double DQN, dueling DQN, prioritized experience replay, and noisy networks for better exploration. DQN was able to learn human-level policies directly from pixels and rewards for many Atari games using the same hyperparameters and network architecture.
This document provides a summary of sampling-based approximations for reinforcement learning. It discusses using samples to approximate value iteration, policy iteration, and Q-learning when the state-action space is too large to store a table of values. Key points covered include using Q-learning with function approximation instead of a table, using features to generalize Q-values across states, and examples of feature representations like those used for the Tetris domain. Convergence properties of approximate Q-learning are also discussed.
The document summarizes key concepts from chapter 2 of the lecture slides on linear algebra for deep learning. It defines scalars as single numbers and vectors as 1-D arrays of numbers that can be indexed. Matrices are 2-D arrays of numbers that are indexed with two numbers. Tensors generalize this to arrays with more dimensions. The document also discusses matrix operations like transpose, dot product, and inversion which are important for solving systems of linear equations. It introduces norms as functions to measure the size of vectors.
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Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
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Speakers:
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13. n OpLmal Control
=
given an MDP (S, A, P, R, γ, H)
find the opLmal policy π*
Outline
n Exact Methods:
n Value Itera*on
n Policy IteraLon
For now: small discrete state-acLon spaces as they are simpler to get the main
concepts across. We will consider large / conLnuous spaces later!
18. n = opLmal value for state s when H=0
n
n = opLmal value for state s when H=1
n
n = opLmal value for state s when H=2
n
n = opLmal value for state s when H = k
n
Value IteraLon
V ⇤
0 (s)
V ⇤
0 (s) = 0 8s
V ⇤
1 (s)
V ⇤
1 (s) = max
a
X
s0
P(s0
|s, a)(R(s, a, s0
) + V ⇤
0 (s0
))
V ⇤
2 (s) = max
a
X
s0
P(s0
|s, a)(R(s, a, s0
) + V ⇤
1 (s0
))
V ⇤
2 (s)
V ⇤
k (s) = max
a
X
s0
P(s0
|s, a)(R(s, a, s0
) + V ⇤
k 1(s0
))
V ⇤
k (s)
35. § Now we know how to act for infinite horizon with discounted rewards!
§ Run value iteraLon Lll convergence.
§ This produces V*, which in turn tells us how to act, namely following:
§ Note: the infinite horizon opLmal policy is staLonary, i.e., the opLmal acLon at
a state s is the same acLon at all Lmes. (Efficient to store!)
Theorem. Value itera*on converges. At convergence, we have found the
op*mal value func*on V* for the discounted infinite horizon problem, which
sa*sfies the Bellman equa*ons
Value IteraLon Convergence
⇡⇤
(s) = arg max
a
X
s0
P(s0
|s, a) [R(s, a, s0
) + V ⇤
(s0
)]
V ⇤
(s) = max
a
X
s0
P(s0
|s, a) [R(s, a, s0
) + V ⇤
(s0
)]
37. n Define the max-norm:
n Theorem: For any two approximaLons U and V
n I.e., any disLnct approximaLons must get closer to each other, so, in parLcular, any approximaLon
must get closer to the true U and value iteraLon converges to a unique, stable, opLmal soluLon
n Theorem:
n I.e. once the change in our approximaLon is small, it must also be close to correct
Convergence and ContracLons
43. Q-Values
Q*(s, a) = expected utility starting in s, taking action a, and (thereafter)
acting optimally
Bellman Equation:
Q-Value Iteration:
Q⇤
k+1(s, a)
X
s0
P(s0
|s, a)(R(s, a, s0
) + max
a0
Q⇤
k(s0
, a0
))
45. n OpLmal Control
=
given an MDP (S, A, P, R, γ, H)
find the opLmal policy π*
Outline
n Exact Methods:
n Value Itera*on
n Policy IteraLon
For now: small discrete state-acLon spaces as they are simpler to get the main
concepts across. We will consider large / conLnuous spaces later!
47. Exercise 2
Consider a stochastic policy ⇡(a|s), where ⇡(a|s) is the probability of taking
action a when in state s. Which of the following is the correct update to perform
policy evaluation for this stochastic policy?
1. V ⇡
k+1(s) maxa
P
s0 P(s0
|s, a) (R(s, a, s0
) + V ⇡
k (s0
))
2. V ⇡
k+1(s)
P
s0
P
a ⇡(a|s)P(s0
|s, a) (R(s, a, s0
) + V ⇡
k (s0
))
3. V ⇡
k+1(s)
P
a ⇡(a|s) maxs0 P(s0
|s, a) (R(s, a, s0
) + V ⇡
k (s0
))
51. n OpLmal Control
=
given an MDP (S, A, P, R, γ, H)
find the opLmal policy π*
Outline
n Exact Methods:
n Value Itera*on
n Policy Itera*on
Limita*ons:
• IteraLon over / storage for all states and acLons: requires small,
discrete state-acLon space
• Update equaLons require access to dynamics model