arXiv subjects

Ruihao Zhu

Publications and source records attributed to Ruihao Zhu.

29 records · Page 2Linked to original sources

arXiv2022

Phase Transitions in Learning and Earning under Price Protection Guarantee

Motivated by the prevalence of ``price protection guarantee", which allows a customer who purchased a product in the past to receive a refund from the seller during the so-called price protection period (typically defined as a certain time window after the purchase date) in case the seller decides to lower the price, we study the impact of such policy on the design of online learning algorithm for data-driven dynamic pricing with initially unknown customer demand. We consider a setting where a firm sells a product over a horizon of $T$ time steps. For this setting, we characterize how the value of $M$, the length of price protection period, can affect the optimal regret of the learning process. We show that the optimal regret is $\tildeΘ(\sqrt{T}+\min\{M,\,T^{2/3}\})$ by first establishing a fundamental impossible regime with novel regret lower bound instances. Then, we propose LEAP, a phased exploration type algorithm for \underline{L}earning and \underline{EA}rning under \underline{P}rice Protection to match this lower bound up to logarithmic factors or even doubly logarithmic factors (when there are only two prices available to the seller). Our results reveal the surprising phase transitions of the optimal regret with respect to $M$. Specifically, when $M$ is not too large, the optimal regret has no major difference when compared to that of the classic setting with no price protection guarantee. We also show that there exists an upper limit on how much the optimal regret can deteriorate when $M$ grows large. Finally, we conduct extensive numerical experiments to show the benefit of LEAP over other heuristic methods for this problem.

stat.ML↗

arXiv2022

Learning to Price Supply Chain Contracts against a Learning Retailer

The rise of big data analytics has automated the decision-making of companies and increased supply chain agility. In this paper, we study the supply chain contract design problem faced by a data-driven supplier who needs to respond to the inventory decisions of the downstream retailer. Both the supplier and the retailer are uncertain about the market demand and need to learn about it sequentially. The goal for the supplier is to develop data-driven pricing policies with sublinear regret bounds under a wide range of possible retailer inventory policies for a fixed time horizon. To capture the dynamics induced by the retailer's learning policy, we first make a connection to non-stationary online learning by following the notion of variation budget. The variation budget quantifies the impact of the retailer's learning strategy on the supplier's decision-making. We then propose dynamic pricing policies for the supplier for both discrete and continuous demand. We also note that our proposed pricing policy only requires access to the support of the demand distribution, but critically, does not require the supplier to have any prior knowledge about the retailer's learning policy or the demand realizations. We examine several well-known data-driven policies for the retailer, including sample average approximation, distributionally robust optimization, and parametric approaches, and show that our pricing policies lead to sublinear regret bounds in all these cases. At the managerial level, we answer affirmatively that there is a pricing policy with a sublinear regret bound under a wide range of retailer's learning policies, even though she faces a learning retailer and an unknown demand distribution. Our work also provides a novel perspective in data-driven operations management where the principal has to learn to react to the learning policies employed by other agents in the system.

cs.LG↗

arXiv2022

Model-Free Non-Stationary RL: Near-Optimal Regret and Applications in Multi-Agent RL and Inventory Control

We consider model-free reinforcement learning (RL) in non-stationary Markov decision processes. Both the reward functions and the state transition functions are allowed to vary arbitrarily over time as long as their cumulative variations do not exceed certain variation budgets. We propose Restarted Q-Learning with Upper Confidence Bounds (RestartQ-UCB), the first model-free algorithm for non-stationary RL, and show that it outperforms existing solutions in terms of dynamic regret. Specifically, RestartQ-UCB with Freedman-type bonus terms achieves a dynamic regret bound of $\widetilde{O}(S^{\frac{1}{3}} A^{\frac{1}{3}} Δ^{\frac{1}{3}} H T^{\frac{2}{3}})$, where $S$ and $A$ are the numbers of states and actions, respectively, $Δ>0$ is the variation budget, $H$ is the number of time steps per episode, and $T$ is the total number of time steps. We further present a parameter-free algorithm named Double-Restart Q-UCB that does not require prior knowledge of the variation budget. We show that our algorithms are \emph{nearly optimal} by establishing an information-theoretical lower bound of $Ω(S^{\frac{1}{3}} A^{\frac{1}{3}} Δ^{\frac{1}{3}} H^{\frac{2}{3}} T^{\frac{2}{3}})$, the first lower bound in non-stationary RL. Numerical experiments validate the advantages of RestartQ-UCB in terms of both cumulative rewards and computational efficiency. We demonstrate the power of our results in examples of multi-agent RL and inventory control across related products.

cs.LG↗

arXiv2022

Safe Data Collection for Offline and Online Policy Learning

Motivated by practical needs of experimentation and policy learning in online platforms, we study the problem of safe data collection. Specifically, our goal is to develop a logging policy that efficiently explores different actions to elicit information while achieving competitive reward with a baseline production policy. We first show that a common practice of mixing the production policy with randomized exploration, despite being safe, is sub-optimal in maximizing information gain. Then, we propose a safe optimal logging policy via a novel water-filling technique for the case when no side information about the actions' expected reward is available. We improve upon this design by considering side information and also extend our approaches to the linear contextual model to account for a large number of actions. Along the way, we analyze how our data logging policies impact errors in off(line)-policy learning and empirically validate the benefit of our design by conducting extensive numerical experiments with synthetic and MNIST datasets. To further demonstrate the generality of our approach, we also consider the safe online learning setting. By adaptively applying our techniques, we develop the Safe Phased-Elimination (SafePE) algorithm that can achieve optimal regret bound with only logarithmic number of policy updates.

cs.LG↗

arXiv2021

Learning to Optimize under Non-Stationarity

We introduce algorithms that achieve state-of-the-art \emph{dynamic regret} bounds for non-stationary linear stochastic bandit setting. It captures natural applications such as dynamic pricing and ads allocation in a changing environment. We show how the difficulty posed by the non-stationarity can be overcome by a novel marriage between stochastic and adversarial bandits learning algorithms. Defining $d,B_T,$ and $T$ as the problem dimension, the \emph{variation budget}, and the total time horizon, respectively, our main contributions are the tuned Sliding Window UCB (\texttt{SW-UCB}) algorithm with optimal $\widetilde{O}(d^{2/3}(B_T+1)^{1/3}T^{2/3})$ dynamic regret, and the tuning free bandit-over-bandit (\texttt{BOB}) framework built on top of the \texttt{SW-UCB} algorithm with best $\widetilde{O}(d^{2/3}(B_T+1)^{1/4}T^{3/4})$ dynamic regret.

cs.LG↗

arXiv2021

Hedging the Drift: Learning to Optimize under Non-Stationarity

We introduce data-driven decision-making algorithms that achieve state-of-the-art \emph{dynamic regret} bounds for non-stationary bandit settings. These settings capture applications such as advertisement allocation, dynamic pricing, and traffic network routing in changing environments. We show how the difficulty posed by the (unknown \emph{a priori} and possibly adversarial) non-stationarity can be overcome by an unconventional marriage between stochastic and adversarial bandit learning algorithms. Our main contribution is a general algorithmic recipe for a wide variety of non-stationary bandit problems. Specifically, we design and analyze the sliding window-upper confidence bound algorithm that achieves the optimal dynamic regret bound for each of the settings when we know the respective underlying \emph{variation budget}, which quantifies the total amount of temporal variation of the latent environments. Boosted by the novel bandit-over-bandit framework that adapts to the latent changes, we can further enjoy the (nearly) optimal dynamic regret bounds in a (surprisingly) parameter-free manner. In addition to the classical exploration-exploitation trade-off, our algorithms leverage the power of the "forgetting principle" in the learning processes, which is vital in changing environments. Our extensive numerical experiments on both synthetic and real world online auto-loan datasets show that our proposed algorithms achieve superior empirical performance compared to existing algorithms.

cs.LG↗

arXiv2021

Meta Dynamic Pricing: Transfer Learning Across Experiments

We study the problem of learning shared structure \emph{across} a sequence of dynamic pricing experiments for related products. We consider a practical formulation where 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 (\emph{meta-exploration}) with the need to leverage the estimated prior to achieve good performance (\emph{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 mis-specified 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 to prior-independent algorithms.

cs.LG↗

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.

cs.LG↗

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.

cs.LG↗

arXiv2018

Learning to Route Efficiently with End-to-End Feedback: The Value of Networked Structure

We introduce efficient algorithms which achieve nearly optimal regrets for the problem of stochastic online shortest path routing with end-to-end feedback. The setting is a natural application of the combinatorial stochastic bandits problem, a special case of the linear stochastic bandits problem. We show how the difficulties posed by the large scale action set can be overcome by the networked structure of the action set. Our approach presents a novel connection between bandit learning and shortest path algorithms. Our main contribution is an adaptive exploration algorithm with nearly optimal instance-dependent regret for any directed acyclic network. We then modify it so that nearly optimal worst case regret is achieved simultaneously. Driven by the carefully designed Top-Two Comparison (TTC) technique, the algorithms are efficiently implementable. We further conduct extensive numerical experiments to show that our proposed algorithms not only achieve superior regret performances, but also reduce the runtime drastically.

cs.LG↗

arXiv2014

PRINCE: Privacy-Preserving Mechanisms for Influence Diffusion in Online Social Networks

This paper has been withdrawn by the author due to a crucial sign error in equation 1. With the advance of online social networks, there has been extensive research on how to spread influence in online social networks, and many algorithms and models have been proposed. However, many fundamental problems have also been overlooked. Among those, the most important problems are the incentive aspect and the privacy aspect (eg, nodes' relationships) of the influence propagation in online social networks. Bearing these defects in mind, and incorporating the powerful tool from differential privacy, we propose PRINCE, which is a series of \underline{PR}ivacy preserving mechanisms for \underline{IN}fluen\underline{CE} diffusion in online social networks to solve the problems. We not only theoretically prove many elegant properties of PRINCE, but also implement PRINCE to evaluate its performance extensively. The evaluation results show that PRINCE achieves good performances. To the best of our knowledge, PRINCE is the first differentially private mechanism for influence diffusion in online social networks.

cs.SI↗