A Risk-Averse Framework for Non-Stationary Stochastic Multi-Armed Bandits

In a typical stochastic multi-armed bandit problem, the objective is often to maximize the expected sum of rewards over some time horizon $T$. While the choice of a strategy that accomplishes that is optimal with no additional information, it is no longer the case when provided additional environment-specific knowledge. In particular, in areas of high volatility like healthcare or finance, a naive reward maximization approach often does not accurately capture the complexity of the learning problem and results in unreliable solutions. To tackle problems of this nature, we propose a framework of adaptive risk-aware strategies that operate in non-stationary environments. Our framework incorporates various risk measures prevalent in the literature to map multiple families of multi-armed bandit algorithms into a risk-sensitive setting. In addition, we equip the resulting algorithms with the Restarted Bayesian Online Change-Point Detection (R-BOCPD) algorithm and impose a (tunable) forced exploration strategy to detect local (per-arm) switches. We provide finite-time theoretical guarantees and an asymptotic regret bound of order $\tilde O(\sqrt{K_T T})$ up to time horizon $T$ with $K_T$ the total number of change-points. In practice, our framework compares favorably to the state-of-the-art in both synthetic and real-world environments and manages to perform efficiently with respect to both risk-sensitivity and non-stationarity

Learning Techniques in Multi-Armed Bandits

Multi-Armed bandit problem is a classic example of the exploration vs. exploitation dilemma in which a collection of one-armed bandits, each with unknown but fixed reward probability, is given. The key idea is to develop a strategy, which results in the arm with the highest reward probability to be played such that the total reward obtained is maximized. Although seemingly a simplistic problem, solution strategies are important because of their wide applicability in a myriad of areas such as adaptive routing, resource allocation, clinical trials, and more recently in the area of online recommendation of news articles, advertisements, coupons, etc. to name a few. In this dissertation, we present different types of Bayesian Inference based bandit algorithms for Two and Multiple Armed Bandits which use Order Statistics to select the next arm to play. The Bayesian strategies, also known in literature as Thompson Method are shown to function well for a whole range of values, including very small values, outperforming UCB and other commonly used strategies. Empirical analysis results show a significant improvement on multiple datasets. In the second part of the dissertation, two types of Successive Reduction (SR) strategies - 1) Successive Reduction Hoeffding (SRH) and 2) Successive Reduction Order Statistics (SRO) are introduced. Both use an Order Statistics based Sampling method for arm selection, and then successively eliminate bandit arms from consideration depending on a confidence threshold. While SRH uses Hoeffding Bounds for elimination, SRO uses the probability of an arm being superior to the currently selected arm to measure confidence. The empirical results show that the performance advantage of proposed SRO scheme increasing persistently with the number of bandit arms while the SRH scheme shows similar performance as pure Thompson Sampling Method. In the third part of the dissertation, the assumption of the reward probability being fixed is removed. We model problems where reward probabilities are drifting , and introduce a new method called Dynamic Thompson Sampling (DTS) which adapts the reward probability estimate faster than traditional schemes and thus leads to improved performance in terms of lower regret. Our empirical results demonstrate that DTS method outperforms the state-of-the-art techniques, namely pure Thompson Sampling, UCB-Normal and UCB-f, for the case of dynamic reward probabilities. Furthermore, the performance advantage of the proposed DTS scheme increases persistently with the number of bandit arms. In the last part of the dissertation, we delve into arm space decomposition and use of multiple agents in the Bandit process. The three most important characteristics of a multi-agent systems are 1) Autonomy --- agents are completely or partially autonomous, 2) Local views --- agents are restricted to a local view of information, and 3) Decentralization of control --- each agent influences a limited part of the overall decision space. We study and compare Centralized vs. Decentralized Sampling Algorithm in Multi-Armed Bandit problems in the context of common payoff games . In the Centralized Decision Making, a central agent maintains a global view of the currently available information and makes a decision to choose the next arm just as the regular Bayesian Algorithm. In Decentralized Decision Making, each agent maintains a local view of the arms and makes decisions just based on the local information available at its end without communicating with other agents. The Decentralized Decision Making is modeled as a Game Theory problem. Our results show that the Decentralized systems perform well for both the cases of Pure as well Mixed Nash equilibria and their performance scales well with the increase in the number of arms due to reduced dimensionality of the space. We thus believe that this dissertation establishes Bayesian Multi-Armed bandit strategies as one of the prominent strategies in the field of bandits and opens up venues for new interesting research in the future

Robust Restless Bandits: Tackling Interval Uncertainty with Deep Reinforcement Learning

We introduce Robust Restless Bandits, a challenging generalization of restless multi-arm bandits (RMAB). RMABs have been widely studied for intervention planning with limited resources. However, most works make the unrealistic assumption that the transition dynamics are known perfectly, restricting the applicability of existing methods to real-world scenarios. To make RMABs more useful in settings with uncertain dynamics: (i) We introduce the Robust RMAB problem and develop solutions for a minimax regret objective when transitions are given by interval uncertainties; (ii) We develop a double oracle algorithm for solving Robust RMABs and demonstrate its effectiveness on three experimental domains; (iii) To enable our double oracle approach, we introduce RMABPPO, a novel deep reinforcement learning algorithm for solving RMABs. RMABPPO hinges on learning an auxiliary "$\lambda$-network" that allows each arm's learning to decouple, greatly reducing sample complexity required for training; (iv) Under minimax regret, the adversary in the double oracle approach is notoriously difficult to implement due to non-stationarity. To address this, we formulate the adversary oracle as a multi-agent reinforcement learning problem and solve it with a multi-agent extension of RMABPPO, which may be of independent interest as the first known algorithm for this setting. Code is available at https://github.com/killian-34/RobustRMAB.Comment: 18 pages, 3 figure

MANAS: Multi-Agent Neural Architecture Search

The Neural Architecture Search (NAS) problem is typically formulated as a graph search problem where the goal is to learn the optimal operations over edges in order to maximise a graph-level global objective. Due to the large architecture parameter space, efficiency is a key bottleneck preventing NAS from its practical use. In this paper, we address the issue by framing NAS as a multi-agent problem where agents control a subset of the network and coordinate to reach optimal architectures. We provide two distinct lightweight implementations, with reduced memory requirements (1/8th of state-of-the-art), and performances above those of much more computationally expensive methods. Theoretically, we demonstrate vanishing regrets of the form O(sqrt(T)), with T being the total number of rounds. Finally, aware that random search is an, often ignored, effective baseline we perform additional experiments on 3 alternative datasets and 2 network configurations, and achieve favourable results in comparison

Promoting Fairness through Hyperparameter Optimization

Considerable research effort has been guided towards algorithmic fairness but real-world adoption of bias reduction techniques is still scarce. Existing methods are either metric- or model-specific, require access to sensitive attributes at inference time, or carry high development or deployment costs. This work explores the unfairness that emerges when optimizing ML models solely for predictive performance, and how to mitigate it with a simple and easily deployed intervention: fairness-aware hyperparameter optimization (HO). We propose and evaluate fairness-aware variants of three popular HO algorithms: Fair Random Search, Fair TPE, and Fairband. We validate our approach on a real-world bank account opening fraud case-study, as well as on three datasets from the fairness literature. Results show that, without extra training cost, it is feasible to find models with 111% mean fairness increase and just 6% decrease in performance when compared with fairness-blind HO.Comment: arXiv admin note: substantial text overlap with arXiv:2010.0366

New Models qnd Algorithms for Bandits and Markets

Inspired by advertising markets, we consider large-scale sequential decision making problems in which a learner must deploy an algorithm to behave optimally under uncertainty. Although many of these problems can be modeled as contextual bandit problems, we argue that the tools and techniques for analyzing bandit problems with large numbers of actions and contexts can be greatly expanded. While convexity and metric-similarity assumptions on the process generating rewards have yielded some algorithms in existing literature, certain types of assumptions that have been fruitful in offline supervised learning settings have yet to even be considered. Notably missing, for example, is any kind of graphical model approach to assuming structured rewards, despite the success such assumptions have achieved in inducing scalable learning and inference with high-dimensional distributions. Similarly, we observe that there are countless tools for understanding the relationship between a choice of model class in supervised learning, and the generalization error of the best fit from that class, such as the celebrated VC-theory. However, an analogous notion of dimensionality, which relates a generic structural assumption on rewards to regret rates in an online optimization problem, is not fully developed. The primary goal of this dissertation, therefore, will be to fill out the space of models, algorithms, and assumptions used in sequential decision making problems. Toward this end, we will develop a theory for bandit problems with structured rewards that permit a graphical model representation. We will give an efficient algorithm for regret-minimization in such a setting, and along the way will develop a deeper connection between online supervised learning and regret-minimization. This dissertation will also introduce a complexity measure for generic structural assumptions on reward functions, which we call the Haystack Dimension. We will prove that the Haystack Dimension characterizes the optimal rates achievable up to log factors. Finally, we will describe more application-oriented techniques for solving problems in advertising markets, which again demonstrate how methods from traditional disciplines, such as statistical survival analysis, can be leveraged to design novel algorithms for optimization in markets

Thirty Years of Machine Learning: The Road to Pareto-Optimal Wireless Networks

Future wireless networks have a substantial potential in terms of supporting a broad range of complex compelling applications both in military and civilian fields, where the users are able to enjoy high-rate, low-latency, low-cost and reliable information services. Achieving this ambitious goal requires new radio techniques for adaptive learning and intelligent decision making because of the complex heterogeneous nature of the network structures and wireless services. Machine learning (ML) algorithms have great success in supporting big data analytics, efficient parameter estimation and interactive decision making. Hence, in this article, we review the thirty-year history of ML by elaborating on supervised learning, unsupervised learning, reinforcement learning and deep learning. Furthermore, we investigate their employment in the compelling applications of wireless networks, including heterogeneous networks (HetNets), cognitive radios (CR), Internet of things (IoT), machine to machine networks (M2M), and so on. This article aims for assisting the readers in clarifying the motivation and methodology of the various ML algorithms, so as to invoke them for hitherto unexplored services as well as scenarios of future wireless networks.Comment: 46 pages, 22 fig