arXiv subjects

Baihe Huang

Publications and source records attributed to Baihe Huang.

27 records · Page 2Linked to original sources

arXiv2023

Evaluating and Incentivizing Diverse Data Contributions in Collaborative Learning

For a federated learning model to perform well, it is crucial to have a diverse and representative dataset. However, the data contributors may only be concerned with the performance on a specific subset of the population, which may not reflect the diversity of the wider population. This creates a tension between the principal (the FL platform designer) who cares about global performance and the agents (the data collectors) who care about local performance. In this work, we formulate this tension as a game between the principal and multiple agents, and focus on the linear experiment design problem to formally study their interaction. We show that the statistical criterion used to quantify the diversity of the data, as well as the choice of the federated learning algorithm used, has a significant effect on the resulting equilibrium. We leverage this to design simple optimal federated learning mechanisms that encourage data collectors to contribute data representative of the global population, thereby maximizing global performance.

cs.GT↗

arXiv2023

A Faster Quantum Algorithm for Semidefinite Programming via Robust IPM Framework

This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang, Song, Tao and Zhang, FOCS 2022]. While, the previous work only provides an efficient implementation in the classical setting. This work provides a novel quantum implementation. We give a quantum second-order algorithm with high-accuracy in both the optimality and the feasibility of its output, and its running time depending on $\log(1/ε)$ on well-conditioned instances. Due to the limitation of quantum itself or first-order method, all the existing quantum SDP solvers either have polynomial error dependence or low-accuracy in the feasibility.

quant-ph↗

arXiv2023

Policy Mirror Descent for Regularized Reinforcement Learning: A Generalized Framework with Linear Convergence

Policy optimization, which finds the desired policy by maximizing value functions via optimization techniques, lies at the heart of reinforcement learning (RL). In addition to value maximization, other practical considerations arise as well, including the need of encouraging exploration, and that of ensuring certain structural properties of the learned policy due to safety, resource and operational constraints. These can often be accounted for via regularized RL, which augments the target value function with a structure-promoting regularizer. Focusing on discounted infinite-horizon Markov decision processes, we propose a generalized policy mirror descent (GPMD) algorithm for solving regularized RL. As a generalization of policy mirror descent (arXiv:2102.00135), our algorithm accommodates a general class of convex regularizers and promotes the use of Bregman divergence in cognizant of the regularizer in use. We demonstrate that our algorithm converges linearly to the global solution over an entire range of learning rates, in a dimension-free fashion, even when the regularizer lacks strong convexity and smoothness. In addition, this linear convergence feature is provably stable in the face of inexact policy evaluation and imperfect policy updates. Numerical experiments are provided to corroborate the appealing performance of GPMD.

cs.LG↗

arXiv2022

Offline Reinforcement Learning with Realizability and Single-policy Concentrability

Sample-efficiency guarantees for offline reinforcement learning (RL) often rely on strong assumptions on both the function classes (e.g., Bellman-completeness) and the data coverage (e.g., all-policy concentrability). Despite the recent efforts on relaxing these assumptions, existing works are only able to relax one of the two factors, leaving the strong assumption on the other factor intact. As an important open problem, can we achieve sample-efficient offline RL with weak assumptions on both factors? In this paper we answer the question in the positive. We analyze a simple algorithm based on the primal-dual formulation of MDPs, where the dual variables (discounted occupancy) are modeled using a density-ratio function against offline data. With proper regularization, we show that the algorithm enjoys polynomial sample complexity, under only realizability and single-policy concentrability. We also provide alternative analyses based on different assumptions to shed light on the nature of primal-dual algorithms for offline RL.

cs.LG↗

arXiv2021

Going Beyond Linear RL: Sample Efficient Neural Function Approximation

Deep Reinforcement Learning (RL) powered by neural net approximation of the Q function has had enormous empirical success. While the theory of RL has traditionally focused on linear function approximation (or eluder dimension) approaches, little is known about nonlinear RL with neural net approximations of the Q functions. This is the focus of this work, where we study function approximation with two-layer neural networks (considering both ReLU and polynomial activation functions). Our first result is a computationally and statistically efficient algorithm in the generative model setting under completeness for two-layer neural networks. Our second result considers this setting but under only realizability of the neural net function class. Here, assuming deterministic dynamics, the sample complexity scales linearly in the algebraic dimension. In all cases, our results significantly improve upon what can be attained with linear (or eluder dimension) methods.

cs.LG↗

arXiv2021

Solving SDP Faster: A Robust IPM Framework and Efficient Implementation

This paper introduces a new robust interior point method analysis for semidefinite programming (SDP). This new robust analysis can be combined with either logarithmic barrier or hybrid barrier. Under this new framework, we can improve the running time of semidefinite programming (SDP) with variable size $n \times n$ and $m$ constraints up to $ε$ accuracy. We show that for the case $m = Ω(n^2)$, we can solve SDPs in $m^ω$ time. This suggests solving SDP is nearly as fast as solving the linear system with equal number of variables and constraints. This is the first result that tall dense SDP can be solved in the nearly-optimal running time, and it also improves the state-of-the-art SDP solver [Jiang, Kathuria, Lee, Padmanabhan and Song, FOCS 2020]. In addition to our new IPM analysis, we also propose a number of techniques that might be of further interest, such as, maintaining the inverse of a Kronecker product using lazy updates, a general amortization scheme for positive semidefinite matrices.

math.OC↗

arXiv2021

Towards General Function Approximation in Zero-Sum Markov Games

This paper considers two-player zero-sum finite-horizon Markov games with simultaneous moves. The study focuses on the challenging settings where the value function or the model is parameterized by general function classes. Provably efficient algorithms for both decoupled and {coordinated} settings are developed. In the {decoupled} setting where the agent controls a single player and plays against an arbitrary opponent, we propose a new model-free algorithm. The sample complexity is governed by the Minimax Eluder dimension -- a new dimension of the function class in Markov games. As a special case, this method improves the state-of-the-art algorithm by a $\sqrt{d}$ factor in the regret when the reward function and transition kernel are parameterized with $d$-dimensional linear features. In the {coordinated} setting where both players are controlled by the agent, we propose a model-based algorithm and a model-free algorithm. In the model-based algorithm, we prove that sample complexity can be bounded by a generalization of Witness rank to Markov games. The model-free algorithm enjoys a $\sqrt{K}$-regret upper bound where $K$ is the number of episodes.

cs.GT↗

arXiv2021

Optimal Gradient-based Algorithms for Non-concave Bandit Optimization

Bandit problems with linear or concave reward have been extensively studied, but relatively few works have studied bandits with non-concave reward. This work considers a large family of bandit problems where the unknown underlying reward function is non-concave, including the low-rank generalized linear bandit problems and two-layer neural network with polynomial activation bandit problem. For the low-rank generalized linear bandit problem, we provide a minimax-optimal algorithm in the dimension, refuting both conjectures in [LMT21, JWWN19]. Our algorithms are based on a unified zeroth-order optimization paradigm that applies in great generality and attains optimal rates in several structured polynomial settings (in the dimension). We further demonstrate the applicability of our algorithms in RL in the generative model setting, resulting in improved sample complexity over prior approaches. Finally, we show that the standard optimistic algorithms (e.g., UCB) are sub-optimal by dimension factors. In the neural net setting (with polynomial activation functions) with noiseless reward, we provide a bandit algorithm with sample complexity equal to the intrinsic algebraic dimension. Again, we show that optimistic approaches have worse sample complexity, polynomial in the extrinsic dimension (which could be exponentially worse in the polynomial degree).

cs.LG↗

arXiv2021

FL-NTK: A Neural Tangent Kernel-based Framework for Federated Learning Convergence Analysis

Federated Learning (FL) is an emerging learning scheme that allows different distributed clients to train deep neural networks together without data sharing. Neural networks have become popular due to their unprecedented success. To the best of our knowledge, the theoretical guarantees of FL concerning neural networks with explicit forms and multi-step updates are unexplored. Nevertheless, training analysis of neural networks in FL is non-trivial for two reasons: first, the objective loss function we are optimizing is non-smooth and non-convex, and second, we are even not updating in the gradient direction. Existing convergence results for gradient descent-based methods heavily rely on the fact that the gradient direction is used for updating. This paper presents a new class of convergence analysis for FL, Federated Learning Neural Tangent Kernel (FL-NTK), which corresponds to overparamterized ReLU neural networks trained by gradient descent in FL and is inspired by the analysis in Neural Tangent Kernel (NTK). Theoretically, FL-NTK converges to a global-optimal solution at a linear rate with properly tuned learning parameters. Furthermore, with proper distributional assumptions, FL-NTK can also achieve good generalization.

cs.LG↗