Wireless communication systems operate in complex time-varying environments. Therefore, selecting the optimal configuration parameters in these systems is a challenging problem. For wireless links, rate selection is used to select the optimal data transmission rate that maximizes the link throughput subject to an application-defined latency constraint. We model rate selection as a stochastic multi-armed bandit (MAB) problem, where a finite set of transmission rates are modeled as independent bandit arms. For this setup, we propose Con-TS, a novel constrained version of the Thompson sampling algorithm, where the latency requirement is modeled by a linear constraint on arm selection probabilities. Since our algorithm learns a Bayesian model of the wireless link, it can be adapted to exploit prior knowledge often available in practical wireless networks. Through numerical results from simulated experiments, we demonstrate that Con-TS significantly outperforms state-of-the-art bandit algorithms proposed in the literature. Further, we compare Con-TS with the outer loop link adaptation (OLLA) scheme, which is the state-of-the-art in practical wireless networks and relies on carefully tuned offline link models. We show that Con-TS outperforms OLLA in simulations, further, it can elegantly incorporate information from the offline link models to substantially improve performance.
Constrained bandit problems have recently been studied in the context of revenue maximization under a finite inventory setting, termed (BwK). @cite_4 , a upper confidence bound (UCB)-based approach was introduced that was shown to be optimal for the stochastic BwK problem. Further in @cite_15 , a Thompson sampling algorithms for budgeted multi-armed bandits was proposed that outperforms the UCB BwK algorithm. Subsequently in @cite_25 , Thompson Sampling was studied for revenue optimization for a finite inventory that contains multiple, non-identical products. In this paper, we formulate the the rate selection problem as an a knapsack problem. To the best of our knowledge, this is a novel formulation of the rate selection problem that provides new insights into its analysis. Further, unlike finite-inventory problems where the inventory costs accrue over time, we show that the latency constraint can be formulated in terms of the expected transmission success probability.
@cite_15 @cite_4 @cite_25
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The multi-armed bandit (MAB) problem features the classical tradeoff between exploration and exploitation. The input specifies several stochastic arms which evolve with each pull, and the goal is to maximize the expected reward after a fixed budget of pulls. The celebrated work of , surveyed in [8], presumes a condition on the arms called the martingale assumption. In [9], A. obtained an LP-based 1 48-approximation for the problem with the martingale assumption removed. We improve the algorithm to a 4 27-approximation, with simpler analysis. Our algorithm also generalizes to the case of MAB superprocesses with (stochastic) multi-period actions. This generalization captures the framework introduced by Guha and Munagala in [11], and yields new results for their budgeted learning problems. Also, we obtain a (1 2 -- e)-approximation for the variant of MAB where preemption (playing an arm, switching to another arm, then coming back to the first arm) is not allowed. This contains the stochastic knapsack problem of Dean, Goemans, and Vondrak in [6] with correlated rewards, where we are given a knapsack of fixed size, and a set of jobs each with a joint distribution for its size and reward. The actual size and reward of a job can only be discovered in real-time as it is being scheduled, and the objective is to maximize expected reward before the knapsack size is exhausted. Our (1 2 -- e)-approximation improves the 1 16 and 1 8 approximations in [9] for correlated stochastic knapsack with cancellation and no cancellation, respectively, providing to our knowledge the first tight algorithm for these problems that matches the integrality gap of 2. We sample probabilities from an exponential-sized dynamic programming solution, whose existence is guaranteed by an LP projection argument. We hope this technique can also be applied to other dynamic programming problems which can be projected down onto a small LP. We consider a network revenue management problem where an online retailer aims to maximize revenue from multiple products with limited inventory constraints. As common in practice, the retailer does not know the consumer's purchase probability at each price and must learn the mean demand from sales data. We propose an efficient and effective dynamic pricing algorithm, which builds upon the Thompson sampling algorithm used for multi-armed bandit problems by incorporating inventory constraints into the model and algorithm. Our algorithm proves to have both strong theoretical performance guarantees as well as promising numerical performance results when compared to other algorithms developed for the same setting. More broadly, our paper contributes to the literature on the multi-armed bandit problem with resource constraints, since our algorithm applies directly to this setting when the inventory constraint is interpreted as general resource constraints. We consider the multi armed bandit problem in non-stationary environments. Based on the Bayesian method, we propose a variant of Thompson Sampling which can be used in both rested and restless bandit scenarios. Applying discounting to the parameters of prior distribution, we describe a way to systematically reduce the effect of past observations. Further, we derive the exact expression for the probability of picking sub-optimal arms. By increasing the exploitative value of Bayes' samples, we also provide an optimistic version of the algorithm. Extensive empirical analysis is conducted under various scenarios to validate the utility of proposed algorithms. A comparison study with various state-of-the-arm algorithms is also included. The restless bandit problem is one of the most well-studied generalizations of the celebrated stochastic multi-armed bandit (MAB) problem in decision theory. In its ultimate generality, the restless bandit problem is known to be PSPACE-Hard to approximate to any nontrivial factor, and little progress has been made on this problem despite its significance in modeling activity allocation under uncertainty. In this article, we consider the Feedback MAB problem, where the reward obtained by playing each of n independent arms varies according to an underlying on off Markov process whose exact state is only revealed when the arm is played. The goal is to design a policy for playing the arms in order to maximize the infinite horizon time average expected reward. This problem is also an instance of a Partially Observable Markov Decision Process (POMDP), and is widely studied in wireless scheduling and unmanned aerial vehicle (UAV) routing. Unlike the stochastic MAB problem, the Feedback MAB problem does not admit to greedy index-based optimal policies. We develop a novel duality-based algorithmic technique that yields a surprisingly simple and intuitive (2+e)-approximate greedy policy to this problem. We show that both in terms of approximation factor and computational efficiency, our policy is closely related to the Whittle index, which is widely used for its simplicity and efficiency of computation. Subsequently we define a multi-state generalization, that we term Monotone bandits, which remains subclass of the restless bandit problem. We show that our policy remains a 2-approximation in this setting, and further, our technique is robust enough to incorporate various side-constraints such as blocking plays, switching costs, and even models where determining the state of an arm is a separate operation from playing it. Our technique is also of independent interest for other restless bandit problems, and we provide an example in nonpreemptive machine replenishment. Interestingly, in this case, our policy provides a constant factor guarantee, whereas the Whittle index is provably polynomially worse. By presenting the first O(1) approximations for nontrivial instances of restless bandits as well as of POMDPs, our work initiates the study of approximation algorithms in both these contexts.