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Multi Armed
Bandit Algorithms
By,
Shrinivas Vasala
Overview
2
- K Slot Machine
- Multi Armed Bandit Problems
- A/B Testing
- MAB Algorithms
- Summary
K Slot Machines
3
- Choose a machine and receive a reward
- T turns (chances)
- What will be your goal ?
- Maximize the cumulative rewards
- How you choose the machines (arms) ?
4
Multi Armed Bandit Problem (MAB)
- Goal : Two Fold
- Try different arms (Exploration)
- Play the seemingly most
rewarding arm (Exploitation)
- Explore – Exploit Trade Off
- Multi Armed Bandit Algorithms
- Reward distribution ( Unknown)
- Mean Reward : <µ1, . . . , µK>
- Standard Deviation Reward: <σ1, . . . , σk>
- Regret :
- Maximize Cumulative Rewards = Minimize Regret
(Minimize)
A/B Testing
5
- Advertisement selection for a request from a pool
of advertisements
- Rewards : CTR/AR or CPM
- Recommendation of news articles to users
- Product pricing and promotional offers
- MAB is used to measure the performance of A/B
Testing experiments
MAB Algorithms
6
- Epsilon-greedy
- Softmax
- Pursuit
- Upper Confidence Bound (UCB1)
- UCB1-Tuned
Epsilon-greedy Algorithm
- Choose epsilon ( Ɛ) : exploration factor
- Play the best arm with probability (1 – Ɛ): Exploitation
- Play the random arm with probability Ɛ: Exploration
Note :
- Typical value of Ɛ = 0.10 (10%)
Softmax Algorithm
8
Pursuit Algorithm
9
Upper Confidence Bound 1 (UCB1)
10
- At each iteration, choose the arm corresponding to maximum above score.
UCB1- Tuned
11
Advanced Bandits
12
- Adversarial Bandits
- Contextual Bandits
- Infinite Armed Bandits
- Thomson Sampling Bandits
Summary
13
- Each algorithm has an upper bound on regret
- It’s a function of average rewards distribution
- Each algorithm has a tuning parameter
- Parameter tuning is a function of reward function
- Choose right MAB algorithm based on
simulations/historical data
- All these algorithms have life time auto learning
mechanism
14
Thank You

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Bandit algorithms

  • 2. Overview 2 - K Slot Machine - Multi Armed Bandit Problems - A/B Testing - MAB Algorithms - Summary
  • 3. K Slot Machines 3 - Choose a machine and receive a reward - T turns (chances) - What will be your goal ? - Maximize the cumulative rewards - How you choose the machines (arms) ?
  • 4. 4 Multi Armed Bandit Problem (MAB) - Goal : Two Fold - Try different arms (Exploration) - Play the seemingly most rewarding arm (Exploitation) - Explore – Exploit Trade Off - Multi Armed Bandit Algorithms - Reward distribution ( Unknown) - Mean Reward : <µ1, . . . , µK> - Standard Deviation Reward: <σ1, . . . , σk> - Regret : - Maximize Cumulative Rewards = Minimize Regret (Minimize)
  • 5. A/B Testing 5 - Advertisement selection for a request from a pool of advertisements - Rewards : CTR/AR or CPM - Recommendation of news articles to users - Product pricing and promotional offers - MAB is used to measure the performance of A/B Testing experiments
  • 6. MAB Algorithms 6 - Epsilon-greedy - Softmax - Pursuit - Upper Confidence Bound (UCB1) - UCB1-Tuned
  • 7. Epsilon-greedy Algorithm - Choose epsilon ( Ɛ) : exploration factor - Play the best arm with probability (1 – Ɛ): Exploitation - Play the random arm with probability Ɛ: Exploration Note : - Typical value of Ɛ = 0.10 (10%)
  • 10. Upper Confidence Bound 1 (UCB1) 10 - At each iteration, choose the arm corresponding to maximum above score.
  • 12. Advanced Bandits 12 - Adversarial Bandits - Contextual Bandits - Infinite Armed Bandits - Thomson Sampling Bandits
  • 13. Summary 13 - Each algorithm has an upper bound on regret - It’s a function of average rewards distribution - Each algorithm has a tuning parameter - Parameter tuning is a function of reward function - Choose right MAB algorithm based on simulations/historical data - All these algorithms have life time auto learning mechanism