13 papers
Learning Fair Allocation of Indivisible Items from Limited Feedback
Xinyu Liu, David Kempe, Evi Micha
We study a setting in which an algorithm must output a fair allocation of indivisible items while "learning on the job". More specifically, the algorithm is to output an allocation…
Beyond Linear Attention: Softmax Transformers Implement In-Context Reinforcement Learning
Zixuan Xie, Xinyu Liu, Claire Chen +3
In-context reinforcement learning (ICRL) studies agents that, after pretraining, adapt to new tasks by conditioning on additional context without parameter updates. Existing theore…
MathlibPR: Pull Request Merge-Readiness Benchmark for Formal Mathematical Libraries
Zixuan Xie, Xinyu Liu, Shangtong Zhang
The ecosystem of Lean and Mathlib has become the de facto standard for large language model (LLM) assisted formal reasoning with remarkable successes in recent years. Those success…
Convergence and Emergence of In-Context Reinforcement Learning with Chain of Thought
Zixuan Xie, Xinyu Liu, Rohan Chandra +1
In-context reinforcement learning (ICRL) refers to the ability of RL agents to adapt to new tasks at inference time without parameter updates by conditioning on additional context.…
Almost Sure Convergence Rates of Stochastic Approximation and Reinforcement Learning via a Poisson-Moreau Drift
Xinyu Liu, Zixuan Xie, Shangtong Zhang
Establishing almost sure convergence rates for stochastic approximation and reinforcement learning under Markovian noise is a fundamental theoretical challenge. We make progress to…
MathlibLemma: Folklore Lemma Generation and Benchmark for Formal Mathematics
Xinyu Liu, Zixuan Xie, Amir Moeini +5
While the ecosystem of Lean and Mathlib has enjoyed celebrated success in formal mathematical reasoning with the help of large language models (LLMs), the absence of many folklore…
Near-Optimal Sparsifiers for Stochastic Knapsack and Assignment Problems
Shaddin Dughmi, Yusuf Hakan Kalayci, Xinyu Liu
When uncertainty meets costly information gathering, a fundamental question emerges: which data points should we probe to unlock near-optimal solutions? Sparsification of stochasti…
Pure Exploration via Frank-Wolfe Self-Play
Xinyu Liu, Chao Qin, Wei You
We study pure exploration in structured stochastic multi-armed bandits, aiming to efficiently identify the correct hypothesis from a finite set of alternatives. For a broad class o…
Extensions of Robbins-Siegmund Theorem with Applications in Reinforcement Learning
Xinyu Liu, Zixuan Xie, Shangtong Zhang
The Robbins-Siegmund theorem establishes the convergence of stochastic processes that are almost supermartingales and is one of the most commonly used approaches for analyzing stoc…
Measurement-Based Quantum Diffusion Models
Xinyu Liu, Jingze Zhuang, Wanda Hou +1
We introduce measurement-based quantum diffusion models that bridge classical and quantum diffusion theory through randomized weak measurements. The measurement-based approach natu…
Finite Sample Analysis of Linear Temporal Difference Learning with Arbitrary Features
Zixuan Xie, Xinyu Liu, Rohan Chandra +1
Linear TD() is one of the most fundamental reinforcement learning algorithms for policy evaluation. Previously, convergence rates are typically established under the assumption…
Linear -Learning Does Not Diverge in : Convergence Rates to a Bounded Set
Xinyu Liu, Zixuan Xie, Shangtong Zhang
-learning is one of the most fundamental reinforcement learning algorithms. It is widely believed that -learning with linear function approximation (i.e., linear -learning…
Almost Sure Convergence Rates and Concentration of Stochastic Approximation and Reinforcement Learning with Markovian Noise
Xiaochi Qian, Zixuan Xie, Xinyu Liu +1
This paper establishes the first almost sure convergence rate and the first maximal concentration bound with exponential tails for general contractive stochastic approximation algo…