Thompson Sampling Research Articles

On the problem of finding the optimal set of computer device protection tools

Protecting a computer device is an important task that requires software implementation, because not every user can choose the right set of security features for their device, and there are not many applications that can help a user choose the right set of security features. In this paper, the authors consider the following tools for finding the optimal strategy for protecting a computer device: the method of Savage, Hurwitz, Bayes, Monte Carlo, Thompson Sampling algorithm. Their features and advantages are highlighted. They are based on a software application that will allow users to calculate the optimal combination of tools designed to protect their computers, depending on the wishes of users and the characteristics of their devices. Such an application can be used by system administrators to select the optimal protection of the entire computer fleet. The authors conducted a series of experiments and comparative analysis of the simulation results. The average search time for an optimal strategy for protecting a computer device is estimated.

Self-tuning portfolio-based Bayesian optimization

Portfolio strategies for Bayesian optimization (BO) aim to mitigate the issue of choosing an acquisition function when performing black-box optimization with Gaussian processes (GP) surrogate models. In that sense, the GP-Hedge is a straightforward portfolio framework commonly used in practice. Our work proposes to overcome existing limitations on the GP-Hedge and related methods, such as reducing the influence of far past evaluations and promoting better exploration. Moreover, we aim to achieve such improvements without sacrificing the practicality of simpler portfolio strategies. More specifically, we propose a new BO method equipped with the aforementioned enhancements enabled by additional self-tuned hyperparameters, which are sampled during the optimization via Thompson sampling. We are able to update the posteriors analytically at each iteration by carefully choosing meaningful conjugate priors. The new approach, named Self-Tuning Portfolio-based BO (SETUP-BO), improves standard portfolio strategies without the need for manually tuning hyperparameters, which preserves easiness of use. We evaluate our method and its competitors in the task of hyperparameter optimization (HPO), a critical step towards automated machine learning (AutoML), following a thorough meta-surrogate benchmarking approach. We also consider a real-world scenario related to the task of fault detection in energy plants. Our methodology achieves promising results, which indicates the viability of the proposed SETUP-BO.

Meta Dynamic Pricing: Transfer Learning Across Experiments

We study the problem of learning shared structure across a sequence of dynamic pricing experiments for related products. We consider a practical formulation in which the unknown demand parameters for each product come from an unknown distribution (prior) that is shared across products. We then propose a meta dynamic pricing algorithm that learns this prior online while solving a sequence of Thompson sampling pricing experiments (each with horizon T) for N different products. Our algorithm addresses two challenges: (i) balancing the need to learn the prior (meta-exploration) with the need to leverage the estimated prior to achieve good performance (meta-exploitation) and (ii) accounting for uncertainty in the estimated prior by appropriately “widening” the estimated prior as a function of its estimation error. We introduce a novel prior alignment technique to analyze the regret of Thompson sampling with a misspecified prior, which may be of independent interest. Unlike prior-independent approaches, our algorithm’s meta regret grows sublinearly in N, demonstrating that the price of an unknown prior in Thompson sampling can be negligible in experiment-rich environments (large N). Numerical experiments on synthetic and real auto loan data demonstrate that our algorithm significantly speeds up learning compared with prior-independent algorithms. This paper was accepted by George J. Shanthikumar, Management Science Special Section on Data-Driven Prescriptive Analytics.

Multi-Interface Channel Allocation in Fog Computing Systems Using Thompson Sampling

In fog computing systems, each fog node often maintains multiple interfaces to achieve simultaneous communications with end devices. To maximize the utilization of network capacities and avoid interference, a critical mission for each fog node is to allocate distinct channels to its interfaces, also known as multi-interface channel allocation, to maximize the total throughput by successful transmissions. However, the effective allocation scheme design is challenging because the full knowledge of channel state dynamics is often hard to attain in practice. Faced with such uncertainties, online learning is needed to cooperate with online decision making. In this article, we devise an integrated design to conduct such multi-interface channel allocation in fog computing systems. Specifically, by formulating the channel allocation problem in the settings of multiarmed bandit with multiple plays and leveraging Thompson sampling techniques, we propose a multi-interface channel allocation with binary feedback (MICA-B) scheme, which makes online channel allocation decisions through effective learning from binary transmission feedback. Our theoretical analysis shows that MICA-B achieves a sublinear O(logT) regret bound on the performance loss (also known as regret) over a finite time horizon T. Based on MICA-B, we further exploit structure information of channel characteristics and design constrained MICA-B (CoMICA-B) to improve learning efficiency. Further, we propose multi-interface channel allocation with multilevel feedback (MICA-M) which extends MICA to handle more general cases with multilevel feedback information. Our simulation results verify the effectiveness and robustness of MICA-B, CoMICA-B, and MICA-M in terms of regret reduction.

Two-Stage Thompson Sampling for Outer-Loop Link Adaptation

In this letter, we consider outer-loop link adaptation, wherein we pursue to find the optimum modulation and coding scheme (MCS) that provides the maximum throughput without directly estimating the channel state. We cast this problem in a form of multi-armed bandit, an online decision making policy based on sequential observations. To efficiently solve a formulated problem, we propose a novel two-stage Thompson sampling. The proposed method is built based on the observation that the optimum MCS level appears in a certain group that satisfies feasibility conditions. Exploiting this feature, we find the optimum MCS level via two stages. In the first stage, we identify a group that has high probability of including the optimum MCS. In the second stage, we only focus on the MCS levels within the identified group in the first stage, and investigate the optimum MCS. By doing this, the search space is significantly reduced, which leads to the performance improvement. Simulation results show that the proposed method outperforms the existing state-of-art algorithm.

An empirical evaluation of active inference in multi-armed bandits

A key feature of sequential decision making under uncertainty is a need to balance between exploiting—choosing the best action according to the current knowledge, and exploring—obtaining information about values of other actions. The multi-armed bandit problem, a classical task that captures this trade-off, served as a vehicle in machine learning for developing bandit algorithms that proved to be useful in numerous industrial applications. The active inference framework, an approach to sequential decision making recently developed in neuroscience for understanding human and animal behaviour, is distinguished by its sophisticated strategy for resolving the exploration–exploitation trade-off. This makes active inference an exciting alternative to already established bandit algorithms. Here we derive an efficient and scalable approximate active inference algorithm and compare it to two state-of-the-art bandit algorithms: Bayesian upper confidence bound and optimistic Thompson sampling. This comparison is done on two types of bandit problems: a stationary and a dynamic switching bandit. Our empirical evaluation shows that the active inference algorithm does not produce efficient long-term behaviour in stationary bandits. However, in the more challenging switching bandit problem active inference performs substantially better than the two state-of-the-art bandit algorithms. The results open exciting venues for further research in theoretical and applied machine learning, as well as lend additional credibility to active inference as a general framework for studying human and animal behaviour.

Seamlessly Unifying Attributes and Items: Conversational Recommendation for Cold-start Users

Static recommendation methods like collaborative filtering suffer from the inherent limitation of performing real-time personalization for cold-start users. Online recommendation, e.g., multi-armed bandit approach, addresses this limitation by interactively exploring user preference online and pursuing the exploration-exploitation (EE) trade-off. However, existing bandit-based methods model recommendation actions homogeneously. Specifically, they only consider the items as the arms, being incapable of handling the item attributes , which naturally provide interpretable information of user’s current demands and can effectively filter out undesired items. In this work, we consider the conversational recommendation for cold-start users, where a system can both ask the attributes from and recommend items to a user interactively. This important scenario was studied in a recent work [54]. However, it employs a hand-crafted function to decide when to ask attributes or make recommendations. Such separate modeling of attributes and items makes the effectiveness of the system highly rely on the choice of the hand-crafted function, thus introducing fragility to the system. To address this limitation, we seamlessly unify attributes and items in the same arm space and achieve their EE trade-offs automatically using the framework of Thompson Sampling. Our Conversational Thompson Sampling (ConTS) model holistically solves all questions in conversational recommendation by choosing the arm with the maximal reward to play. Extensive experiments on three benchmark datasets show that ConTS outperforms the state-of-the-art methods Conversational UCB (ConUCB) [54] and Estimation—Action—Reflection model [27] in both metrics of success rate and average number of conversation turns.

The Perils of Misspecified Priors and Optional Stopping in Multi-Armed Bandits.

The connection between optimal stopping times of American Options and multi-armed bandits is the subject of active research. This article investigates the effects of optional stopping in a particular class of multi-armed bandit experiments, which randomly allocates observations to arms proportional to the Bayesian posterior probability that each arm is optimal (Thompson sampling). The interplay between optional stopping and prior mismatch is examined. We propose a novel partitioning of regret into peri/post testing. We further show a strong dependence of the parameters of interest on the assumed prior probability density.

Maximizing the Efficiency of Active Case Finding for SARS-CoV-2 Using Bandit Algorithms.

Even as vaccination for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) expands in the United States, cases will linger among unvaccinated individuals for at least the next year, allowing the spread of the coronavirus to continue in communities across the country. Detecting these infections, particularly asymptomatic ones, is critical to stemming further transmission of the virus in the months ahead. This will require active surveillance efforts in which these undetected cases are proactively sought out rather than waiting for individuals to present to testing sites for diagnosis. However, finding these pockets of asymptomatic cases (i.e., hotspots) is akin to searching for needles in a haystack as choosing where and when to test within communities is hampered by a lack of epidemiological information to guide decision makers' allocation of these resources. Making sequential decisions with partial information is a classic problem in decision science, the explore v. exploit dilemma. Using methods-bandit algorithms-similar to those used to search for other kinds of lost or hidden objects, from downed aircraft or underground oil deposits, we can address the explore v. exploit tradeoff facing active surveillance efforts and optimize the deployment of mobile testing resources to maximize the yield of new SARS-CoV-2 diagnoses. These bandit algorithms can be implemented easily as a guide to active case finding for SARS-CoV-2. A simple Thompson sampling algorithm and an extension of it to integrate spatial correlation in the data are now embedded in a fully functional prototype of a web app to allow policymakers to use either of these algorithms to target SARS-CoV-2 testing. In this instance, potential testing locations were identified by using mobility data from UberMedia to target high-frequency venues in Columbus, Ohio, as part of a planned feasibility study of the algorithms in the field. However, it is easily adaptable to other jurisdictions, requiring only a set of candidate test locations with point-to-point distances between all locations, whether or not mobility data are integrated into decision making in choosing places to test.

Bayesian Algorithms for Decentralized Stochastic Bandits

We study a decentralized cooperative multi-agent multi-armed bandit (MAB) problem with K arms and N agents connected over a network. In this model, each arm's reward distribution is the same for every agent, and rewards are drawn independently across agents and over time steps. At each iteration, agents independently choose an arm to play and exchange at most poly(K) real-valued messages with their neighbors. Existing lower bound on the average per-agent regret over the network shows that cooperation with other agents can achieve a reduction of O(\frac 1N) over when playing in isolation. Motivated by this, we study a message-passing algorithm that can be combined with existing Bayesian MAB algorithms. Using this, we propose a decentralized Thompson Sampling (TS) algorithm and a decentralized Bayes-UCB algorithm. Under decentralized TS for bounded rewards, we establish a problem-dependent upper bound on the average per-agent regret in terms of the number of agents in the network and the network topology. For Bernoulli rewards, our upper bound asymptotically matches the lower bound. We empirically show that the proposed decentralized TS algorithm incurs significantly lesser per-agent regret than previously proposed algorithms. Furthermore, we show that the proposed decentralized TS can be extended to general bandit problems, where posterior distribution cannot be computed in closed form. We combine our decentralized TS algorithm with Variational Inference to apply our proposed algorithm to complex realistic reward distributions in a computationally efficient manner. We implement our proposed decentralized TS under gossip protocol and over time-varying networks, where each communication link has a fixed probability of failure and show that it incurs logarithmic regret.

Distributed Learning-Based Cache Replacement in Collaborative Edge Networks

In this letter, distributed content caching is considered in a collaborative edge caching system where a central infostation broadcasts information about the content migration to all edge nodes. Each edge node is equipped with a small base station for fetching the requested contents from its neighbouring edge nodes and with a storage unit for caching the contents. To achieve efficient content caching and collaboration, an online decision-making problem of maximizing the cache-hit-ratio whilst ensuring the end users’ quality-of-experience (QoE) is formulated. Furthermore, it is assumed that the content popularity knowledge is not available in advance and has to be leaned regularly over time in an online manner. To this end, we propose a distributed online content-popularity leaning algorithm based on Thompson sampling for updating the cache storage units in real-time. Simulation results demonstrate that the proposed algorithm outperforms the benchmarks in terms of the cache-hit-ratio and QoE in the long run.

Efficient Optimal Selection for Composited Advertising Creatives with Tree Structure

Ad creatives are one of the prominent mediums for online e-commerce advertisements. Ad creatives with enjoyable visual appearance may increase the click-through rate (CTR) of products. Ad creatives are typically handcrafted by advertisers and then delivered to the advertising platforms for advertisement. In recent years, advertising platforms are capable of instantly compositing ad creatives with arbitrarily designated elements of each ingredient, so advertisers are only required to provide basic materials. While facilitating the advertisers, a great number of potential ad creatives can be composited, making it difficult to accurately estimate CTR for them given limited real-time feedback. To this end, we propose an Adaptive and Efficient ad creative Selection (AES) framework based on a tree structure. The tree structure on compositing ingredients enables dynamic programming for efficient ad creative selection on the basis of CTR. Due to limited feedback, the CTR estimator is usually of high variance. Exploration techniques based on Thompson sampling are widely used for reducing variances of the CTR estimator, alleviating feedback sparsity. Based on the tree structure, Thompson sampling is adapted with dynamic programming, leading to efficient exploration for potential ad creatives with the largest CTR. We finally evaluate the proposed algorithm on the synthetic dataset and the real-world dataset. The results show that our approach can outperform competing baselines in terms of convergence rate and overall CTR.

Mercer Features for Efficient Combinatorial Bayesian Optimization

Bayesian optimization (BO) is an efficient framework for solving black-box optimization problems with expensive function evaluations. This paper addresses the BO problem setting for combinatorial spaces (e.g., sequences and graphs) that occurs naturally in science and engineering applications. A prototypical example is molecular optimization guided by expensive experiments. The key challenge is to balance the complexity of statistical models and tractability of search to select combinatorial structures for evaluation. In this paper, we propose an efficient approach referred as Mercer Features for Combinatorial Bayesian Optimization (MerCBO). The key idea behind MerCBO is to provide explicit feature maps for diffusion kernels over discrete objects by exploiting the structure of their combinatorial graph representation. These Mercer features combined with Thompson sampling as the acquisition function allows us to employ efficient solvers for finding the next structure for evaluation. Experimental evaluation on diverse real-world benchmarks demonstrates that MerCBO performs similarly or better than prior methods.

Improved Worst-Case Regret Bounds for Randomized Least-Squares Value Iteration

This paper studies regret minimization with randomized value functions in reinforcement learning. In tabular finite-horizon Markov Decision Processes, we introduce a clipping variant of one classical Thompson Sampling (TS)-like algorithm, randomized least-squares value iteration (RLSVI). Our $\tilde{\mathrm{O}}(H^2S\sqrt{AT})$ high-probability worst-case regret bound improves the previous sharpest worst-case regret bounds for RLSVI and matches the existing state-of-the-art worst-case TS-based regret bounds.

Lenient Regret for Multi-Armed Bandits

We consider the Multi-Armed Bandit (MAB) problem, where an agent sequentially chooses actions and observes rewards for the actions it took. While the majority of algorithms try to minimize the regret, i.e., the cumulative difference between the reward of the best action and the agent's action, this criterion might lead to undesirable results. For example, in large problems, or when the interaction with the environment is brief, finding an optimal arm is infeasible, and regret-minimizing algorithms tend to over-explore. To overcome this issue, algorithms for such settings should instead focus on playing near-optimal arms. To this end, we suggest a new, more lenient, regret criterion that ignores suboptimality gaps smaller than some ε. We then present a variant of the Thompson Sampling (TS) algorithm, called ε-TS, and prove its asymptotic optimality in terms of the lenient regret. Importantly, we show that when the mean of the optimal arm is high enough, the lenient regret of ε-TS is bounded by a constant. Finally, we show that ε-TS can be applied to improve the performance when the agent knows a lower bound of the suboptimality gaps.

Computing an Efficient Exploration Basis for Learning with Univariate Polynomial Features

Barycentric spanners have been used as an efficient exploration basis in online linear optimization problems in a bandit framework. We characterise the barycentric spanner for decision problems in which the cost (or reward) is a polynomial in a single decision variable. Our characterisation of the barycentric spanner is two-fold: we show that the barycentric spanner under a polynomial cost function is the unique solution to a set of nonlinear algebraic equations, as well as the solution to a convex optimization problem. We provide numerical results to show that our method computes the barycentric spanner for the polynomial case significantly faster than the only other known algorithm for the purpose. As an application, we consider a dynamic pricing problem in which the revenue is an unknown polynomial function of the price. We then empirically show that the use of a barycentric spanner to initialise the prior distribution in a Thompson sampling setting leads to lower cumulative regret as compared to standard initialisations. We also illustrate the importance of barycentric spanners in adversarial settings by showing, both theoretically and empirically, that a barycentric spanner achieves the minimax value in a static adversarial linear regression problem where the learner selects the training points while an adversary selects the testing points and controls the variance of the noise corrupting the training samples

Variable Selection Via Thompson Sampling

–Thompson sampling is a heuristic algorithm for the multi-armed bandit problem which has a long tradition in machine learning. The algorithm has a Bayesian spirit in the sense that it selects arms based on posterior samples of reward probabilities of each arm. By forging a connection between combinatorial binary bandits and spike-and-slab variable selection, we propose a stochastic optimization approach to subset selection called Thompson variable selection (TVS). TVS is a framework for interpretable machine learning which does not rely on the underlying model to be linear. TVS brings together Bayesian reinforcement and machine learning in order to extend the reach of Bayesian subset selection to nonparametric models and large datasets with very many predictors and/or very many observations. Depending on the choice of a reward, TVS can be deployed in offline as well as online setups with streaming data batches. Tailoring multiplay bandits to variable selection, we provide regret bounds without necessarily assuming that the arm mean rewards be unrelated. We show a very strong empirical performance on both simulated and real data. Unlike deterministic optimization methods for spike-and-slab variable selection, the stochastic nature makes TVS less prone to local convergence and thereby more robust.

Online Learning-Based Reconfigurable Antenna Mode Selection Exploiting Channel Correlation

Reconfigurable antennas (RAs) emerged as a promising technology that can deal with channel variations and enhance the capacity and reliability of the wireless channel. To fully exploit the advantage of RAs, optimal antenna modes need to be selected in an online manner. However, the channel statistics are unknown a priori. Multi-armed bandit-based online learning algorithms were proposed to address this challenge, but the main drawback of existing approaches are that their regret scales linearly with the number of antenna modes, which converges slowly when the latter is large. To improve the scalability, we first apply an existing algorithm: Thompson sampling via Gaussian process (TS-GP), and propose two new algorithms for antenna mode selection: upper confidence bound with channel prediction (UCB-CP) and Thompson Sampling with channel prediction (TS-CP). TS-GP uses Gaussian prior to model the reward distribution of each antenna mode, as well as the correlation among them. UCB-CP and TS-CP exploit channel modeling to predict the channel conditions of unexplored antenna modes at each time step, by relating the correlation between different channel states to the underlying antenna modes. We prove the finite-time regret bound of UCB-CP and show that it is independent from the number of arms, when the expected channel estimation errors are small enough. We also extend the algorithms to the mobile setting. Both simulation results and real-world experiments show that all of our proposed learning algorithms can significantly improve the convergence rate and yield much lower regret (thus higher throughput) than existing schemes.

Comparing Epsilon Greedy and Thompson Sampling model for Multi-Armed Bandit algorithm on Marketing Dataset

A/B checking is a regular measure in many marketing procedures for e-Commerce companies. Through well-designed A/B research, advertisers can gain insight about when and how marketing efforts can be maximized and active promotions driven. Whilst many algorithms for the problem are theoretically well developed, empirical confirmation is typically restricted. In practical terms, standard A/B experimentation makes less money relative to more advanced machine learning methods. This paper presents a thorough empirical study of the most popular multi-strategy algorithms. Three important observations can be made from our results. First, simple heuristics such as Epsilon Greedy and Thompson Sampling outperform theoretically sound algorithms in most settings by a significant margin. In this report, the state of A/B testing is addressed, some typical A/B learning algorithms (Multi-Arms Bandits) used to optimize A/B testing are described and comparable. We found that Epsilon Greedy, be an exceptional winner to optimize payouts in this situation.

Alternative models and randomization techniques for Bayesian response-adaptive randomization with binary outcomes.

Bayesian response-adaptive designs, which data adaptively alter the allocation ratio in favor of the better performing treatment, are often criticized for engendering a non-trivial probability of a subject imbalance in favor of the inferior treatment, inflating type I error rate, and increasing sample size requirements. The implementation of these designs using the Thompson sampling methods has generally assumed a simple beta-binomial probability model in the literature; however, the effect of these choices on the resulting design operating characteristics relative to other reasonable alternatives has not been fully examined. Motivated by the Advanced R2 Eperfusion STrategies for Refractory Cardiac Arrest trial, we posit that a logistic probability model coupled with an urn or permuted block randomization method will alleviate some of the practical limitations engendered by the conventional implementation of a two-arm Bayesian response-adaptive design with binary outcomes. In this article, we discuss up to what extent this solution works and when it does not. A computer simulation study was performed to evaluate the relative merits of a Bayesian response-adaptive design for the Advanced R2 Eperfusion STrategies for Refractory Cardiac Arrest trial using the Thompson sampling methods based on a logistic regression probability model coupled with either an urn or permuted block randomization method that limits deviations from the evolving target allocation ratio. The different implementations of the response-adaptive design were evaluated for type I error rate control across various null response rates and power, among other performance metrics. The logistic regression probability model engenders smaller average sample sizes with similar power, better control over type I error rate, and more favorable treatment arm sample size distributions than the conventional beta-binomial probability model, and designs using the alternative randomization methods have a negligible chance of a sample size imbalance in the wrong direction. Pairing the logistic regression probability model with either of the alternative randomization methods results in a much improved response-adaptive design in regard to important operating characteristics, including type I error rate control and the risk of a sample size imbalance in favor of the inferior treatment.