arXiv subjects

Wang Chi Cheung

Publications and source records attributed to Wang Chi Cheung.

23 records · Page 2Linked to original sources

arXiv2020

Reinforcement Learning for Non-Stationary Markov Decision Processes: The Blessing of (More) Optimism

We consider un-discounted reinforcement learning (RL) in Markov decision processes (MDPs) under drifting non-stationarity, i.e., both the reward and state transition distributions are allowed to evolve over time, as long as their respective total variations, quantified by suitable metrics, do not exceed certain variation budgets. We first develop the Sliding Window Upper-Confidence bound for Reinforcement Learning with Confidence Widening (SWUCRL2-CW) algorithm, and establish its dynamic regret bound when the variation budgets are known. In addition, we propose the Bandit-over-Reinforcement Learning (BORL) algorithm to adaptively tune the SWUCRL2-CW algorithm to achieve the same dynamic regret bound, but in a parameter-free manner, i.e., without knowing the variation budgets. Notably, learning non-stationary MDPs via the conventional optimistic exploration technique presents a unique challenge absent in existing (non-stationary) bandit learning settings. We overcome the challenge by a novel confidence widening technique that incorporates additional optimism.

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arXiv2020

Best Arm Identification for Cascading Bandits in the Fixed Confidence Setting

We design and analyze CascadeBAI, an algorithm for finding the best set of $K$ items, also called an arm, within the framework of cascading bandits. An upper bound on the time complexity of CascadeBAI is derived by overcoming a crucial analytical challenge, namely, that of probabilistically estimating the amount of available feedback at each step. To do so, we define a new class of random variables (r.v.'s) which we term as left-sided sub-Gaussian r.v.'s; these are r.v.'s whose cumulant generating functions (CGFs) can be bounded by a quadratic only for non-positive arguments of the CGFs. This enables the application of a sufficiently tight Bernstein-type concentration inequality. We show, through the derivation of a lower bound on the time complexity, that the performance of CascadeBAI is optimal in some practical regimes. Finally, extensive numerical simulations corroborate the efficacy of CascadeBAI as well as the tightness of our upper bound on its time complexity.

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arXiv2020

Non-Stationary Reinforcement Learning: The Blessing of (More) Optimism

We consider un-discounted reinforcement learning (RL) in Markov decision processes (MDPs) under temporal drifts, ie, both the reward and state transition distributions are allowed to evolve over time, as long as their respective total variations, quantified by suitable metrics, do not exceed certain variation budgets. This setting captures the endogeneity, exogeneity, uncertainty, and partial feedback in sequential decision-making scenarios, and finds applications in vehicle remarketing and real-time bidding. We first develop the Sliding Window Upper-Confidence bound for Reinforcement Learning with Confidence Widening (SWUCRL2-CW) algorithm, and establish its dynamic regret bound when the variation budgets are known. In addition, we propose the Bandit-over-Reinforcement Learning (BORL) algorithm to adaptively tune the SWUCRL2-CW algorithm to achieve the same dynamic regret bound, but in a parameter-free manner, ie, without knowing the variation budgets. Finally, we conduct numerical experiments to show that our proposed algorithms achieve superior empirical performance compared to existing algorithms. Notably, the interplay between endogeneity and exogeneity presents a unique challenge, absent in existing (stationary and non-stationary) stochastic online learning settings, when we apply the conventional Optimism in Face of Uncertainty principle to design algorithms with provably low dynamic regret for RL in drifting MDPs. We overcome the challenge by a novel confidence widening technique that incorporates additional optimism into our learning algorithms to ensure low dynamic regret bounds. To extend our theoretical findings, we apply our framework to inventory control problems, and demonstrate how one can alternatively leverage special structures on the state transition distributions to bypass the difficulty in exploring time-varying environments.

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arXiv2019

Exploration-Exploitation Trade-off in Reinforcement Learning on Online Markov Decision Processes with Global Concave Rewards

We consider an agent who is involved in a Markov decision process and receives a vector of outcomes every round. Her objective is to maximize a global concave reward function on the average vectorial outcome. The problem models applications such as multi-objective optimization, maximum entropy exploration, and constrained optimization in Markovian environments. In our general setting where a stationary policy could have multiple recurrent classes, the agent faces a subtle yet consequential trade-off in alternating among different actions for balancing the vectorial outcomes. In particular, stationary policies are in general sub-optimal. We propose a no-regret algorithm based on online convex optimization (OCO) tools (Agrawal and Devanur 2014) and UCRL2 (Jaksch et al. 2010). Importantly, we introduce a novel gradient threshold procedure, which carefully controls the switches among actions to handle the subtle trade-off. By delaying the gradient updates, our procedure produces a non-stationary policy that diversifies the outcomes for optimizing the objective. The procedure is compatible with a variety of OCO tools.

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arXiv2017

Assortment Optimization under Unknown MultiNomial Logit Choice Models

Motivated by e-commerce, we study the online assortment optimization problem. The seller offers an assortment, i.e. a subset of products, to each arriving customer, who then purchases one or no product from her offered assortment. A customer's purchase decision is governed by the underlying MultiNomial Logit (MNL) choice model. The seller aims to maximize the total revenue in a finite sales horizon, subject to resource constraints and uncertainty in the MNL choice model. We first propose an efficient online policy which incurs a regret $\tilde{O}(T^{2/3})$, where $T$ is the number of customers in the sales horizon. Then, we propose a UCB policy that achieves a regret $\tilde{O}(T^{1/2})$. Both regret bounds are sublinear in the number of assortments.

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