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Register a new userMulti-armed Bandit Algorithms on System-on-Chip: Go Frequentist or Bayesian?
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Multi-armed Bandit (MAB) algorithms identify the best arm among multiple arms via exploration-exploitation trade-off without prior knowledge of arm statistics. Their usefulness in wireless radio, IoT, and robotics demand deployment on edge devices, and hence, a mapping on system-on-chip (SoC) is desired. Theoretically, the Bayesian approach-based Thompson Sampling (TS) algorithm offers better performance than the frequentist approach-based Upper Confidence Bound (UCB) algorithm. However, TS is not synthesizable due to Beta function. We address this problem by approximating it via a pseudo-random number generator-based approach and efficiently realize the TS algorithm on Zynq SoC. In practice, the type of arms distribution (e.g., Bernoulli, Gaussian, etc.) is unknown and hence, a single algorithm may not be optimal. We propose a reconfigurable and intelligent MAB (RI-MAB) framework. Here, intelligence enables the identification of appropriate MAB algorithms for a given environment, and reconfigurability allows on-the-fly switching between algorithms on the SoC. This eliminates the need for parallel implementation of algorithms resulting in huge savings in resources and power consumption. We analyze the functional correctness, area, power, and execution time of the proposed and existing architectures for various arm distributions, word-length, and hardware-software co-design approaches. We demonstrate the superiority of the RI-MAB over TS and UCB only architectures.
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In this paper, we consider several finite-horizon Bayesian multi-armed bandit problems with side constraints which are computationally intractable (NP-Hard) and for which no optimal (or near optimal) algorithms are known to exist with sub-exponential running time. All of these problems violate the standard exchange property, which assumes that the reward from the play of an arm is not contingent upon when the arm is played. Not only are index policies suboptimal in these contexts, there has been little analysis of such policies in these problem settings. We show that if we consider near-optimal policies, in the sense of approximation algorithms, then there exists (near) index policies. Conceptually, if we can find policies that satisfy an approximate version of the exchange property, namely, that the reward from the play of an arm depends on when the arm is played to within a constant factor, then we have an avenue towards solving these problems. However such an approximate version of the idling bandit property does not hold on a per-play basis and are shown to hold in a global sense. Clearly, such a property is not necessarily true of arbitrary single arm policies and finding such single arm policies is nontrivial. We show that by restricting the state spaces of arms we can find single arm policies and that these single arm policies can be combined into global (near) index policies where the approximate version of the exchange property is true in expectation. The number of different bandit problems that can be addressed by this technique already demonstrate its wide applicability.
We consider a multi-round auction setting motivated by pay-per-click auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. Initially, neither the auctioneer nor the advertisers have any information about the likelihood of clicks on the advertisements. The auctioneers goal is to design a (dominant strategies) truthful mechanism that (approximately) maximizes the social welfare. If the advertisers bid their true private values, our problem is equivalent to the multi-armed bandit problem, and thus can be viewed as a strategic version of the latter. In particular, for both problems the quality of an algorithm can be characterized by regret, the difference in social welfare between the algorithm and the benchmark which always selects the same best advertisement. We investigate how the design of multi-armed bandit algorithms is affected by the restriction that the resulting mechanism must be truthful. We find that truthful mechanisms have certain strong structural properties -- essentially, they must separate exploration from exploitation -- and they incur much higher regret than the optimal multi-armed bandit algorithms. Moreover, we provide a truthful mechanism which (essentially) matches our lower bound on regret.
Restless Multi-Armed Bandits (RMABs) have been popularly used to model limited resource allocation problems. Recently, these have been employed for health monitoring and intervention planning problems. However, the existing approaches fail to account for the arrival of new patients and the departure of enrolled patients from a treatment program. To address this challenge, we formulate a streaming bandit (S-RMAB) framework, a generalization of RMABs where heterogeneous arms arrive and leave under possibly random streams. We propose a new and scalable approach to computing index-based solutions. We start by proving that index values decrease for short residual lifetimes, a phenomenon that we call index decay. We then provide algorithms designed to capture index decay without having to solve the costly finite horizon problem, thereby lowering the computational complexity compared to existing methods.We evaluate our approach via simulations run on real-world data obtained from a tuberculosis intervention planning task as well as multiple other synthetic domains. Our algorithms achieve an over 150x speed-up over existing methods in these tasks without loss in performance. These findings are robust across multiple domains.
The early sections of this paper present an analysis of a Markov decision model that is known as the multi-armed bandit under the assumption that the utility function of the decision maker is either linear or exponential. The analysis includes efficient procedures for computing the expected utility associated with the use of a priority policy and for identifying a priority policy that is optimal. The methodology in these sections is novel, building on the use of elementary row operations. In the later sections of this paper, the analysis is adapted to accommodate constraints that link the bandits.
Identifying the best arm of a multi-armed bandit is a central problem in bandit optimization. We study a quantum computational version of this problem with coherent oracle access to states encoding the reward probabilities of each arm as quantum amplitudes. Specifically, we show that we can find the best arm with fixed confidence using $tilde{O}bigl(sqrt{sum_{i=2}^nDelta^{smash{-2}}_i}bigr)$ quantum queries, where $Delta_{i}$ represents the difference between the mean reward of the best arm and the $i^text{th}$-best arm. This algorithm, based on variable-time amplitude amplification and estimation, gives a quadratic speedup compared to the best possible classical result. We also prove a matching quantum lower bound (up to poly-logarithmic factors).
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