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NON-STATIONARY BANDIT CHANGE DETECTION-BASED THOMPSON SAMPLING ALGORITHM: A REVIEW
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NON-STATIONARY BANDIT CHANGE DETECTION-BASED THOMPSON SAMPLING ALGORITHM: A REVIEW
1.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 10 Issue: 04 | Apr 2023 www.irjet.net p-ISSN: 2395-0072 © 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 365 NON-STATIONARY BANDIT CHANGE DETECTION-BASED THOMPSON SAMPLING ALGORITHM: A REVIEW Md Arif1, Mr. Nadeem Ahmad2 1M.Tech, Electronic and Communication Engineering, GITM, Lucknow, India 2Assistant Professor Electronic and Communication Engineering, GITM, Lucknow, India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - Thompson Sampling (TS) is a popular algorithm used in multi-armed bandit problems. In the standard setting, it assumes that the rewards associated with each arm are stationary, which means that the reward distributionremains fixed throughout the experiment. However, in manyreal-world scenarios, the reward distribution can change over time, and this is known as a non-stationary bandit problem. In this case, the traditional TS algorithm may not performwell. Toaddress this issue, several extensions of the standard TS algorithm have been proposed for non-stationary bandits. One such extension is the Bayesian Online Changepoint Detection (BOCD) algorithm. BOCD uses a Bayesian frameworktomodel the changes in reward distribution and adjust the exploration and exploitation trade-off accordingly. The BOCD algorithm maintains a posterior distribution over the possible locations of the change points in the reward distribution. At each time step, it uses this posterior to compute the probability that a change point has occurred. If the probability of achangepoint is high, the algorithm explores more to adapt to the new reward distribution. Otherwise, it exploits more to maximize its expected reward. Another extension of the standard TS algorithm for non- stationary bandits is the Dynamic Thompson Sampling (DTS) algorithm. DTS uses a sliding window approach to detect changes in the reward distribution. Thealgorithmmaintainsa separate posterior distribution for each window and selects the arm with the highest expected reward based on the posterior distribution of the current window. In summary, Thompson Sampling is a powerful algorithm for the multi- armed bandit problem, and several extensions can be used to handle non-stationary bandits. These extensions allow the algorithm to adapt to changes in the reward distribution over time and continue to make optimal decisions. Key Words: Sampling, Algorithm for Non-Stationary Bandits, Stationary Bandits, detection based. 1. INTRODUCTION The multi-armed bandit (MAB) framework is a classic problem in decision theory and reinforcement learning. It involves an agent (or decision-maker) who must choose between a set of actions (often called "arms"), each of which has an unknown reward distribution. Thegoal oftheagentis to maximize its cumulativerewardovertimewhilebalancing the exploration of new actions with the exploitation of actions that have already been found to be rewarding. One common example of the MAB problem is the slot machine or "one-armed bandit" problem. In this scenario, the agent must choose between pulling the levers of several slot machines, each of which has a different payout distribution. The agent must decide how many times to pull each lever to maximize its total payout. There are many variations of the MAB problem, each with differentassumptionsandobjectives.Onecommonapproach is the epsilon-greedy algorithm, which chooses the action with the highest estimated reward with probability 1- epsilon, and chooses a random action with probability epsilon. This balances the exploitation of known rewarding actions with the exploration of new actions. Other popular algorithms for the MAB problem include UCB1, Thompson Sampling, and EXP3. These algorithms differ in their assumptionsaboutthedistributionof rewards, and their strategies for balancing exploration and exploitation. The MAB problem has many applications in fields such as advertising, finance, and healthcare. For example, in online advertising, advertisers must decide which ads to display to maximize click-through rates while balancing the need to explore new ads with the need to exploit effective ads. 2. UPPER CONFIDENCE BOUND (UCB) ALGORITHM The Upper Confidence Bound (UCB) algorithm is a popular algorithm for multi-armed bandit problems, which are a class of sequential decision-making problems. In the multi- armed bandit problem, a decision maker must repeatedly choose between a set of actions (or "arms") with uncertain rewards, to maximize their total reward over time. The UCB algorithm works by balancing the exploration of different actions with their potential rewards. At each time step, the algorithm choosestheactionwiththehighestupper confidence bound, which is a measure of the uncertainty of the estimated reward for that action. The upper confidence bound is calculated as the sum of two terms: the estimated reward for the action and a confidence interval term that takes into account the uncertainty in the
2.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 10 Issue: 04 | Apr 2023 www.irjet.net p-ISSN: 2395-0072 © 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 366 estimate. The confidence interval term typically grows over time to ensure that the algorithm continues to explore new actions, even as the estimates of the rewards for existing actions become more certain. By balancing exploration and exploitation in this way, the UCB algorithm can achieve good performance in a wide range of multi-armed bandit problems. 3. ALGORITHM- DISCOUNTED THOMPSON SAMPLING (DTS) Discounted Thompson Sampling (DTS) is a decision-making algorithm that is often used in the context of online advertising, recommendation systems, and other settings where there is uncertainty about the effectiveness of different actions or choices. DTS isa modification ofthewell- known Thompson Sampling algorithm, which is a Bayesian approach to decision-making that has been widely used in machine learning and artificial intelligence. The basic idea behind DTS is to take into account the fact that the value of future rewards may decreaseovertime, due to factors such as discounting or decay. This means that it may be more important to take action now, rather than waiting for more information to become available. To incorporate thisidea intothe ThompsonSamplingalgorithm, DTS uses a discount factor that reduces the weight given to future rewards. In DTS, each action or choice is associated with a probability distribution over the possible rewards. At each step of the algorithm, a random sample is drawn from each of these distributions, and the action with the highest sample is chosen. The distribution for each action is updated based on the observed reward, usingBayesianinference.Thediscount factor is applied to the observed reward before it is used to update the distribution. One of the advantages of DTS is that it can handle non- stationary environments,wheretheunderlying probabilities or reward distributions may change over time. The discount factor allows the algorithm to adjust to these changes, by placing more weight on recent observations. DTS is effective in a variety of applications, including online advertising and recommendation systems. However, like all decision-making algorithms, itseffectivenessdependson the specific context and the quality of the input data. 3.1.Stochastic Bandits Stochastic banditsarea classofdecision-makingproblemsin which an agent must select actions from a set of options or arms, with uncertain rewards associated with each arm. In other words, the agent doesn't know the true reward distribution of each arm, but it can explore by taking different actions and observing the resulting rewards. The goal of the agent is to maximize the total reward it receives over a certain period, or to minimize the regret, which is the difference between the expected reward if the agent had chosen the optimal arm from the beginning and the actual reward obtained. There are several algorithms to solve stochastic bandit problems, including the epsilon-greedy, UCB (Upper ConfidenceBound),andThompsonsampling.Epsilon-greedy is a simple algorithm that selects the best arm with probability 1-epsilon and a random arm with probability epsilon. UCB is a more sophisticated algorithm thatbalances exploration and exploitation by selecting arms with the highest upper confidence bounds. Thompson sampling is a Bayesian algorithm that randomly samples reward distributions for each arm and selects the arm with the highest expected reward according to the samples. Stochastic bandits have numerous applications in various fields, including recommender systems, online advertising, and clinical trials. Figure-1: Stochastic Bandits 4. LITERATURE REVIEW In the section of the literature review, we have studied the previous research paper related to Thompson sampling for different decision-making, the summary of all previous research papers is given below: Joseph: Every genuinely autonomous system must have the capacity to make choices. One approachtofindingsuchways is via experience-based learning of decision-making strategies, since this kind of learning may help uncover strategies that are robust against the influence of noise and flexible enough to be used in a variety of settings. The multi- armed bandit problem and the best arm identification problem have been used as starting points for our exploration of this area (and related variations). After much
3.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 10 Issue: 04 | Apr 2023 www.irjet.net p-ISSN: 2395-0072 © 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 367 trial and error, we've found that Thompson Sampling is an effective method for dealing with the multi-armed bandit algorithm. This solution is optimal for the Bernoulli armed bandit issue because it meets the lower restriction on anticipated cumulative regret. In many circumstances, the cost of computing is minimal. By using conjugate priors, MCMC, or variational methods, Thompson Sampling may be used to model a broad range of decision-making settings, including contextual bandit issues. It is adaptable to include cross-hand dependencies and is resistant to reward delays. To extend the evidence of Agrawal and Goyal to the optimistic variant of the approach, we make certain adjustments to optimism such that it also fulfills the lower limit for cumulative regret. As an additional finding, we find that the Normal Thompson Sampling approach (one that employs the Normal distribution as the conjugate prior) outperforms the more standard Thompson Sampling strategy (which employs a Beta prior) in terms of empirical performance. Mellor, Jonathan: Many methods that combine Thompson Sampling with Change Point detectionhavebeenexploredin this work. In their designated roles, we have shown their utility. Bandit scenarios using real-world data sets like the Yahoo! dataset and the Foreign Exchange further highlight their usefulness. They are shown to fail the PASCAL challenge when pitted against comparably complex but carefully calibrated competing algorithms. Our research, however, lends credence to a pair of methods that are analogous to Adapt-EvE but only keep tabsonchangestothe "best" arm: Global-CTS2 and PA-CTS2. Due to its adaptability, the model holds out possibilities for further improvement via theintroductionofadditional assumptions. It's also worth notingthatotherrewarddistributions beyond Bernoulli's are completely OK. False alarms are a common issue with change point detection methods, but a Bayesian approach might help avoid them. Given thattheyarederived from fundamental models, the algorithms have theoretical support; nonetheless, further research is needed before a complete theoretical account of their performance can be provided. Alami: We propose Global-STS-CF, an extension of the Switching Corrupt Bandit Problem using three distinct Thompson Sam plings. The experimental results demonstrate the superior performance of the suggested method. Notably, Global-STS-CF competes with an oracle, Corrupted Feedback, that is aware of the inflection points in advance, posing a challenge to Thompson sampling. These outcomes are a directconsequenceofGlobal-STS-foundation CF's in the Bayesian idea of following the most knowledgeable individuals throughout the world, which enables us to detect and react to shifts in the landscape with remarkable efficiency. Bykeepinganexpertdistributionona per-arm basis, the suggested approach may be easily adapted to the Per-arm Switching Corrupted Multi-Armed Bandit. Next, we'll examine the Global-STS-CF via the lens of pseudo-cumulative regret. Gourab: To keep tabs on the dynamic two-armed bandit problem environment, we investigate a change-detection- based Thompson Sampling approach (TS-CD). We have established the minimumstationaryregimetimewindowfor TS-CD, making it possible to detect the transitionsassoonas they occur. Our results show that the proposed TS-CD algorithm converges to asymptotic optimality over a wide range of update rates. To test the efficacy of the strategy, we apply it to the RAT selection problem at the wireless network's edge. We have shownthatTS-CDissuperiortothe standard max power band selection method and other bandit algorithms designedforunpredictable environments. Maarten: We have investigated the OLTR issueina dynamic setting where user tastes change quickly. Here, we provide cascading non-stationary bandits, an online-learning variation of the widely-used cascade model (CM) for predicting users' click behaviors. It has been suggested that the algorithms CascadeDUCB and CascadeSWUCBbeused to solve it. They are proven to experience sub-linear remorse by our theoretical analysis. Our experimental results on the Yandex click dataset corroborate these theoretical predictions. Many new paths for the development of mobile OLTR are opened up. To begin with, we have just thought about the CM configuration. Futureresearchshouldtakeinto account other click modelssuchasDBN [ChapelleandZhang, 2009] that can process multiple clicks. The second area of interest was UCB-based policy. One alternative is to apply a policy from the softmax family [Besbes et al., 2014]. In this direction, it is possible to get upperlimitsthatareinsensitive to the number of transitions. Giuseppe: We put forward a novel bandit method to solve the issue of learning in dynamic settings. The algorithm demonstrated superior performance over state-of-the-art solutions and the ability to adapt to various patterns of nonstationarity. All-Season is also far easier to useandmore sturdy than its competitors, making it well-suited for use in industrial settings and requiring less upkeep. We speculate that there is more work to be done in addressing the model misspecification issue and choosing whichmodelsshouldbe eliminated. In particular, we think that constructing the posterior prediction weights using the General Bayes technique (Knoblauch et al., 2019) might be a more robust option. Gourab et.al: To account for the unpredictability of real- world environments, we provide a KS-test-based change detection technique in the context of the Multi-Agent-Based (MAB) architecture. We use our KS-test-inspired, actively adaptable TS algorithm, TS-KS, for the MAB problem. TS-KS has a sub-linear regret in the two-armedbanditproblem.It's important to note that the proposed approach may detect a change even when more sophisticated methods based on mean estimates fail. As seen in two instances, we
4.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 10 Issue: 04 | Apr 2023 www.irjet.net p-ISSN: 2395-0072 © 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 368 demonstrate that the TS-KS algorithm outperforms boththe actively adaptiveTS-CDtechniqueandthepassivelyadaptive D-TS strategy. To add, the results of the portfolio optimization case study demonstrate that TS-KS is competitive with other leading forecasting algorithms, like Facebook-PROPHET and ARIMA. Zhang: Due to the inherent uncertainty of real-world settings, we provide a KS-test-based change detection approach within the framework of the Multi-Agent-Based (MAB) architecture. As an application of our KS-test- inspired, actively adaptiveTSalgorithm,TS-KS,wetacklethe MAB issue. In the two-armed bandit dilemma, TS-KS experiences a sub-linear regret. Note that the suggested technique may succeed when more advanced approaches based on mean estimation fail to spot a shift. Using two examples, we show that the TS-KS algorithm outperforms the active TS-CD method and the passive D-TS approach. Furthermore, the portfolio optimization case study shows that TS-KS can hold its own against other top forecasting algorithms like Facebook-PROPHET and ARIMA. 5. CONCLUSION After studying the above literature review, we found some conclusion, that is given here. Thompson sampling, also known as the Bayesian bandit algorithm, is a popular algorithm used for decision-making problems in various fields such as marketing, medicine, and engineering. It is a probabilistic algorithm that balances exploration and exploitation to find the optimal solution for a givenproblem. Thompson sampling can be used to optimize decision- making in roboticsapplicationssuchasautonomousvehicles and drones. Thompson sampling can be usedtooptimizethe recommendation process in recommender systems by choosing the most relevant items to recommend to users. 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