arXiv subjects

Pan Xu

Publications and source records attributed to Pan Xu.

At least 55 records · Page 3Linked to original sources

arXiv2024

Provable and Practical: Efficient Exploration in Reinforcement Learning via Langevin Monte Carlo

We present a scalable and effective exploration strategy based on Thompson sampling for reinforcement learning (RL). One of the key shortcomings of existing Thompson sampling algorithms is the need to perform a Gaussian approximation of the posterior distribution, which is not a good surrogate in most practical settings. We instead directly sample the Q function from its posterior distribution, by using Langevin Monte Carlo, an efficient type of Markov Chain Monte Carlo (MCMC) method. Our method only needs to perform noisy gradient descent updates to learn the exact posterior distribution of the Q function, which makes our approach easy to deploy in deep RL. We provide a rigorous theoretical analysis for the proposed method and demonstrate that, in the linear Markov decision process (linear MDP) setting, it has a regret bound of $\tilde{O}(d^{3/2}H^{3/2}\sqrt{T})$, where $d$ is the dimension of the feature mapping, $H$ is the planning horizon, and $T$ is the total number of steps. We apply this approach to deep RL, by using Adam optimizer to perform gradient updates. Our approach achieves better or similar results compared with state-of-the-art deep RL algorithms on several challenging exploration tasks from the Atari57 suite.

cs.LG↗

arXiv2024

Distributionally Robust Off-Dynamics Reinforcement Learning: Provable Efficiency with Linear Function Approximation

We study off-dynamics Reinforcement Learning (RL), where the policy is trained on a source domain and deployed to a distinct target domain. We aim to solve this problem via online distributionally robust Markov decision processes (DRMDPs), where the learning algorithm actively interacts with the source domain while seeking the optimal performance under the worst possible dynamics that is within an uncertainty set of the source domain's transition kernel. We provide the first study on online DRMDPs with function approximation for off-dynamics RL. We find that DRMDPs' dual formulation can induce nonlinearity, even when the nominal transition kernel is linear, leading to error propagation. By designing a $d$-rectangular uncertainty set using the total variation distance, we remove this additional nonlinearity and bypass the error propagation. We then introduce DR-LSVI-UCB, the first provably efficient online DRMDP algorithm for off-dynamics RL with function approximation, and establish a polynomial suboptimality bound that is independent of the state and action space sizes. Our work makes the first step towards a deeper understanding of the provable efficiency of online DRMDPs with linear function approximation. Finally, we substantiate the performance and robustness of DR-LSVI-UCB through different numerical experiments.

cs.LG↗

arXiv2024

Tight Competitive and Variance Analyses of Matching Policies in Gig Platforms

In this paper, we propose an online-matching-based model to tackle the two fundamental issues, matching and pricing, existing in a wide range of real-world gig platforms, including ride-hailing (matching riders and drivers), crowdsourcing markets (pairing workers and tasks), and online recommendations (offering items to customers). Our model assumes the arriving distributions of dynamic agents (e.g., riders, workers, and buyers) are accessible in advance, and they can change over time, which is referred to as \emph{Known Heterogeneous Distributions} (KHD). In this paper, we initiate variance analysis for online matching algorithms under KHD. Unlike the popular competitive-ratio (CR) metric, the variance of online algorithms' performance is rarely studied due to inherent technical challenges, though it is well linked to robustness. We focus on two natural parameterized sampling policies, denoted by $\mathsf{ATT}(γ)$ and $\mathsf{SAMP}(γ)$, which appear as foundational bedrock in online algorithm design. We offer rigorous competitive ratio (CR) and variance analyses for both policies. Specifically, we show that $\mathsf{ATT}(γ)$ with $γ\in [0,1/2]$ achieves a CR of $γ$ and a variance of $γ\cdot (1-γ) \cdot B$ on the total number of matches with $B$ being the total matching capacity. In contrast, $\mathsf{SAMP}(γ)$ with $γ\in [0,1]$ accomplishes a CR of $γ(1-γ)$ and a variance of $\barγ (1-\barγ)\cdot B$ with $\barγ=\min(γ,1/2)$. All CR and variance analyses are tight and unconditional of any benchmark. As a byproduct, we prove that $\mathsf{ATT}(γ=1/2)$ achieves an optimal CR of $1/2$.

cs.DS↗

arXiv2024

Wasserstein Distributionally Robust Policy Evaluation and Learning for Contextual Bandits

Off-policy evaluation and learning are concerned with assessing a given policy and learning an optimal policy from offline data without direct interaction with the environment. Often, the environment in which the data are collected differs from the environment in which the learned policy is applied. To account for the effect of different environments during learning and execution, distributionally robust optimization (DRO) methods have been developed that compute worst-case bounds on the policy values assuming that the distribution of the new environment lies within an uncertainty set. Typically, this uncertainty set is defined based on the KL divergence around the empirical distribution computed from the logging dataset. However, the KL uncertainty set fails to encompass distributions with varying support and lacks awareness of the geometry of the distribution support. As a result, KL approaches fall short in addressing practical environment mismatches and lead to over-fitting to worst-case scenarios. To overcome these limitations, we propose a novel DRO approach that employs the Wasserstein distance instead. While Wasserstein DRO is generally computationally more expensive compared to KL DRO, we present a regularized method and a practical (biased) stochastic gradient descent method to optimize the policy efficiently. We also provide a theoretical analysis of the finite sample complexity and iteration complexity for our proposed method. We further validate our approach using a public dataset that was recorded in a randomized stoke trial.

cs.LG↗

arXiv2023

Finite-Time Frequentist Regret Bounds of Multi-Agent Thompson Sampling on Sparse Hypergraphs

We study the multi-agent multi-armed bandit (MAMAB) problem, where $m$ agents are factored into $ρ$ overlapping groups. Each group represents a hyperedge, forming a hypergraph over the agents. At each round of interaction, the learner pulls a joint arm (composed of individual arms for each agent) and receives a reward according to the hypergraph structure. Specifically, we assume there is a local reward for each hyperedge, and the reward of the joint arm is the sum of these local rewards. Previous work introduced the multi-agent Thompson sampling (MATS) algorithm \citep{verstraeten2020multiagent} and derived a Bayesian regret bound. However, it remains an open problem how to derive a frequentist regret bound for Thompson sampling in this multi-agent setting. To address these issues, we propose an efficient variant of MATS, the $ε$-exploring Multi-Agent Thompson Sampling ($ε$-MATS) algorithm, which performs MATS exploration with probability $ε$ while adopts a greedy policy otherwise. We prove that $ε$-MATS achieves a worst-case frequentist regret bound that is sublinear in both the time horizon and the local arm size. We also derive a lower bound for this setting, which implies our frequentist regret upper bound is optimal up to constant and logarithm terms, when the hypergraph is sufficiently sparse. Thorough experiments on standard MAMAB problems demonstrate the superior performance and the improved computational efficiency of $ε$-MATS compared with existing algorithms in the same setting.

cs.LG↗

arXiv2023

New bounds for $b$-Symbol Distances of Matrix Product Codes

Matrix product codes are generalizations of some well-known constructions of codes, such as Reed-Muller codes, $[u+v,u-v]$-construction, etc. Recently, a bound for the symbol-pair distance of a matrix product code was given in \cite{LEL}, and new families of MDS symbol-pair codes were constructed by using this bound. In this paper, we generalize this bound to the $b$-symbol distance of a matrix product code and determine all minimum $b$-symbol distances of Reed-Muller codes. We also give a bound for the minimum $b$-symbol distance of codes obtained from the $[u+v,u-v]$-construction, and use this bound to construct some $[2n,2n-2]_q$-linear $b$-symbol almost MDS codes with arbitrary length. All the minimum $b$-symbol distances of $[n,n-1]_q$-linear codes and $[n,n-2]_q$-linear codes for $1\leq b\leq n$ are determined. Some examples are presented to illustrate these results.

cs.IT↗

arXiv2023

Two-Sided Capacitated Submodular Maximization in Gig Platforms

In this paper, we propose three generic models of capacitated coverage and, more generally, submodular maximization to study task-worker assignment problems that arise in a wide range of gig economy platforms. Our models incorporate the following features: (1) Each task and worker can have an arbitrary matching capacity, which captures the limited number of copies or finite budget for the task and the working capacity of the worker; (2) Each task is associated with a coverage or, more generally, a monotone submodular utility function. Our objective is to design an allocation policy that maximizes the sum of all tasks' utilities, subject to capacity constraints on tasks and workers. We consider two settings: offline, where all tasks and workers are static, and online, where tasks are static while workers arrive dynamically. We present three LP-based rounding algorithms that achieve optimal approximation ratios of $1-1/\mathsf{e} \sim 0.632$ for offline coverage maximization, competitive ratios of $(19-67/\mathsf{e}^3)/27\sim 0.580$ and $0.436$ for online coverage and online monotone submodular maximization, respectively.

cs.DS↗

arXiv2023

Queer In AI: A Case Study in Community-Led Participatory AI

We present Queer in AI as a case study for community-led participatory design in AI. We examine how participatory design and intersectional tenets started and shaped this community's programs over the years. We discuss different challenges that emerged in the process, look at ways this organization has fallen short of operationalizing participatory and intersectional principles, and then assess the organization's impact. Queer in AI provides important lessons and insights for practitioners and theorists of participatory methods broadly through its rejection of hierarchy in favor of decentralization, success at building aid and programs by and for the queer community, and effort to change actors and institutions outside of the queer community. Finally, we theorize how communities like Queer in AI contribute to the participatory design in AI more broadly by fostering cultures of participation in AI, welcoming and empowering marginalized participants, critiquing poor or exploitative participatory practices, and bringing participation to institutions outside of individual research projects. Queer in AI's work serves as a case study of grassroots activism and participatory methods within AI, demonstrating the potential of community-led participatory methods and intersectional praxis, while also providing challenges, case studies, and nuanced insights to researchers developing and using participatory methods.

cs.CY↗

arXiv2022

Global Convergence of Localized Policy Iteration in Networked Multi-Agent Reinforcement Learning

We study a multi-agent reinforcement learning (MARL) problem where the agents interact over a given network. The goal of the agents is to cooperatively maximize the average of their entropy-regularized long-term rewards. To overcome the curse of dimensionality and to reduce communication, we propose a Localized Policy Iteration (LPI) algorithm that provably learns a near-globally-optimal policy using only local information. In particular, we show that, despite restricting each agent's attention to only its $κ$-hop neighborhood, the agents are able to learn a policy with an optimality gap that decays polynomially in $κ$. In addition, we show the finite-sample convergence of LPI to the global optimal policy, which explicitly captures the trade-off between optimality and computational complexity in choosing $κ$. Numerical simulations demonstrate the effectiveness of LPI.

cs.LG↗

arXiv2022

Equity Promotion in Public Transportation

There are many news articles reporting the obstacles confronting poverty-stricken households in access to public transits. These barriers create a great deal of inconveniences for these impoverished families and more importantly, they contribute a lot of social inequalities. A typical approach addressing the issue is to build more transport infrastructure to offer more opportunities to access the public transits especially for those deprived communities. Examples include adding more bus lines connecting needy residents to railways systems and extending existing bus lines to areas with low socioeconomic status. Recently, a new strategy is proposed, which is to harness the ubiquitous ride-hailing services to connect disadvantaged households with the nearest public transportations. Compared with the former infrastructure-based solution, the ride-hailing-based strategy enjoys a few exclusive benefits such as higher effectiveness and more flexibility. In this paper, we propose an optimization model to study how to integrate the two approaches together for equity-promotion purposes. Specifically, we aim to design a strategy of allocating a given limited budget to different candidate programs such that the overall social equity is maximized, which is defined as the minimum covering ratio among all pre-specified protected groups of households (based on race, income, etc.). We have designed a linear-programming (LP) based rounding algorithm, which proves to achieve an optimal approximation ratio of 1-1/e. Additionally, we test our algorithm against a few baselines on real data assembled by outsourcing multiple public datasets collected in the city of Chicago. Experimental results confirm our theoretical predictions and demonstrate the effectiveness of our LP-based strategy in promoting social equity, especially when the budget is insufficient.

cs.AI↗

arXiv2022

A Finite Time Analysis of Two Time-Scale Actor Critic Methods

Actor-critic (AC) methods have exhibited great empirical success compared with other reinforcement learning algorithms, where the actor uses the policy gradient to improve the learning policy and the critic uses temporal difference learning to estimate the policy gradient. Under the two time-scale learning rate schedule, the asymptotic convergence of AC has been well studied in the literature. However, the non-asymptotic convergence and finite sample complexity of actor-critic methods are largely open. In this work, we provide a non-asymptotic analysis for two time-scale actor-critic methods under non-i.i.d. setting. We prove that the actor-critic method is guaranteed to find a first-order stationary point (i.e., $\|\nabla J(\boldsymbolθ)\|_2^2 \le ε$) of the non-concave performance function $J(\boldsymbolθ)$, with $\mathcal{\tilde{O}}(ε^{-2.5})$ sample complexity. To the best of our knowledge, this is the first work providing finite-time analysis and sample complexity bound for two time-scale actor-critic methods.

cs.LG↗

arXiv2022

Exploring the Tradeoff between Competitive Ratio and Variance in Online-Matching Markets

In this paper, we propose an online-matching-based model to study the assignment problems arising in a wide range of online-matching markets, including online recommendations, ride-hailing platforms, and crowdsourcing markets. It features that each assignment can request a random set of resources and yield a random utility, and the two (cost and utility) can be arbitrarily correlated with each other. We present two linear-programming-based parameterized policies to study the tradeoff between the \emph{competitive ratio} (CR) on the total utilities and the \emph{variance} on the total number of matches (unweighted version). The first one (SAMP) is to sample an edge according to the distribution extracted from the clairvoyant optimal, while the second (ATT) features a time-adaptive attenuation framework that leads to an improvement over the state-of-the-art competitive-ratio result. We also consider the problem under a large-budget assumption and show that SAMP achieves asymptotically optimal performance in terms of competitive ratio.

cs.GT↗

arXiv2022

Langevin Monte Carlo for Contextual Bandits

We study the efficiency of Thompson sampling for contextual bandits. Existing Thompson sampling-based algorithms need to construct a Laplace approximation (i.e., a Gaussian distribution) of the posterior distribution, which is inefficient to sample in high dimensional applications for general covariance matrices. Moreover, the Gaussian approximation may not be a good surrogate for the posterior distribution for general reward generating functions. We propose an efficient posterior sampling algorithm, viz., Langevin Monte Carlo Thompson Sampling (LMC-TS), that uses Markov Chain Monte Carlo (MCMC) methods to directly sample from the posterior distribution in contextual bandits. Our method is computationally efficient since it only needs to perform noisy gradient descent updates without constructing the Laplace approximation of the posterior distribution. We prove that the proposed algorithm achieves the same sublinear regret bound as the best Thompson sampling algorithms for a special case of contextual bandits, viz., linear contextual bandits. We conduct experiments on both synthetic data and real-world datasets on different contextual bandit models, which demonstrates that directly sampling from the posterior is both computationally efficient and competitive in performance.

cs.LG↗

arXiv2022

Finite-Time Regret of Thompson Sampling Algorithms for Exponential Family Multi-Armed Bandits

We study the regret of Thompson sampling (TS) algorithms for exponential family bandits, where the reward distribution is from a one-dimensional exponential family, which covers many common reward distributions including Bernoulli, Gaussian, Gamma, Exponential, etc. We propose a Thompson sampling algorithm, termed ExpTS, which uses a novel sampling distribution to avoid the under-estimation of the optimal arm. We provide a tight regret analysis for ExpTS, which simultaneously yields both the finite-time regret bound as well as the asymptotic regret bound. In particular, for a $K$-armed bandit with exponential family rewards, ExpTS over a horizon $T$ is sub-UCB (a strong criterion for the finite-time regret that is problem-dependent), minimax optimal up to a factor $\sqrt{\log K}$, and asymptotically optimal, for exponential family rewards. Moreover, we propose ExpTS$^+$, by adding a greedy exploitation step in addition to the sampling distribution used in ExpTS, to avoid the over-estimation of sub-optimal arms. ExpTS$^+$ is an anytime bandit algorithm and achieves the minimax optimality and asymptotic optimality simultaneously for exponential family reward distributions. Our proof techniques are general and conceptually simple and can be easily applied to analyze standard Thompson sampling with specific reward distributions.

stat.ML↗

arXiv2021

Online minimum matching with uniform metric and random arrivals

We consider Online Minimum Bipartite Matching under the uniform metric. We show that Randomized Greedy achieves a competitive ratio equal to $(1+1/n) (H_{n+1}-1)$, which matches the lower bound. Comparing with the fact that RG achieves an optimal ratio of $Θ(\ln n)$ for the same problem but under the adversarial order, we find that the weaker arrival assumption of random order doesn't offer any extra algorithmic advantage for RG, or make the model strictly more tractable.

cs.DS↗

arXiv2021

Adaptive Sampling for Heterogeneous Rank Aggregation from Noisy Pairwise Comparisons

In heterogeneous rank aggregation problems, users often exhibit various accuracy levels when comparing pairs of items. Thus a uniform querying strategy over users may not be optimal. To address this issue, we propose an elimination-based active sampling strategy, which estimates the ranking of items via noisy pairwise comparisons from users and improves the users' average accuracy by maintaining an active set of users. We prove that our algorithm can return the true ranking of items with high probability. We also provide a sample complexity bound for the proposed algorithm which is better than that of non-active strategies in the literature. Experiments are provided to show the empirical advantage of the proposed methods over the state-of-the-art baselines.

cs.LG↗

arXiv2021

Fairness Maximization among Offline Agents in Online-Matching Markets

Matching markets involve heterogeneous agents (typically from two parties) who are paired for mutual benefit. During the last decade, matching markets have emerged and grown rapidly through the medium of the Internet. They have evolved into a new format, called Online Matching Markets (OMMs), with examples ranging from crowdsourcing to online recommendations to ridesharing. There are two features distinguishing OMMs from traditional matching markets. One is the dynamic arrival of one side of the market: we refer to these as online agents while the rest are offline agents. Examples of online and offline agents include keywords (online) and sponsors (offline) in Google Advertising; workers (online) and tasks (offline) in Amazon Mechanical Turk (AMT); riders (online) and drivers (offline when restricted to a short time window) in ridesharing. The second distinguishing feature of OMMs is the real-time decision-making element. However, studies have shown that the algorithms making decisions in these OMMs leave disparities in the match rates of offline agents. For example, tasks in neighborhoods of low socioeconomic status rarely get matched to gig workers, and drivers of certain races/genders get discriminated against in matchmaking. In this paper, we propose online matching algorithms which optimize for either individual or group-level fairness among offline agents in OMMs. We present two linear-programming (LP) based sampling algorithms, which achieve online competitive ratios at least 0.725 for individual fairness maximization (IFM) and 0.719 for group fairness maximization (GFM), respectively. We conduct extensive numerical experiments and results show that our boosted version of sampling algorithms are not only conceptually easy to implement but also highly effective in practical instances of fairness-maximization-related models.

cs.GT↗

arXiv2021

Sample Efficient Policy Gradient Methods with Recursive Variance Reduction

Improving the sample efficiency in reinforcement learning has been a long-standing research problem. In this work, we aim to reduce the sample complexity of existing policy gradient methods. We propose a novel policy gradient algorithm called SRVR-PG, which only requires $O(1/ε^{3/2})$ episodes to find an $ε$-approximate stationary point of the nonconcave performance function $J(\boldsymbolθ)$ (i.e., $\boldsymbolθ$ such that $\|\nabla J(\boldsymbolθ)\|_2^2\leqε$). This sample complexity improves the existing result $O(1/ε^{5/3})$ for stochastic variance reduced policy gradient algorithms by a factor of $O(1/ε^{1/6})$. In addition, we also propose a variant of SRVR-PG with parameter exploration, which explores the initial policy parameter from a prior probability distribution. We conduct numerical experiments on classic control problems in reinforcement learning to validate the performance of our proposed algorithms.

cs.LG↗