Jing Yang

Songtao Feng, Ming Yin, Ruiquan Huang et al. · princeton

General function approximation is a powerful tool to handle large state and action spaces in a broad range of reinforcement learning (RL) scenarios. However, theoretical understanding of non-stationary MDPs with general function approximation is still limited. In this paper, we make the first such an attempt. We first propose a new complexity metric called dynamic Bellman Eluder (DBE) dimension for non-stationary MDPs, which subsumes majority of existing tractable RL problems in static MDPs as well as non-stationary MDPs. Based on the proposed complexity metric, we propose a novel confidence-set based model-free algorithm called SW-OPEA, which features a sliding window mechanism and a new confidence set design for non-stationary MDPs. We then establish an upper bound on the dynamic regret for the proposed algorithm, and show that SW-OPEA is provably efficient as long as the variation budget is not significantly large. We further demonstrate via examples of non-stationary linear and tabular MDPs that our algorithm performs better in small variation budget scenario than the existing UCB-type algorithms. To the best of our knowledge, this is the first dynamic regret analysis in non-stationary MDPs with general function approximation.

Xizixiang Wei, Cong Shen, Jing Yang et al.

We propose a novel communication design, termed random orthogonalization, for federated learning (FL) in a massive multiple-input and multiple-output (MIMO) wireless system. The key novelty of random orthogonalization comes from the tight coupling of FL and two unique characteristics of massive MIMO -- channel hardening and favorable propagation. As a result, random orthogonalization can achieve natural over-the-air model aggregation without requiring transmitter side channel state information (CSI) for the uplink phase of FL, while significantly reducing the channel estimation overhead at the receiver. We extend this principle to the downlink communication phase and develop a simple but highly effective model broadcast method for FL. We also relax the massive MIMO assumption by proposing an enhanced random orthogonalization design for both uplink and downlink FL communications, that does not rely on channel hardening or favorable propagation. Theoretical analyses with respect to both communication and machine learning performance are carried out. In particular, an explicit relationship among the convergence rate, the number of clients, and the number of antennas is established. Experimental results validate the effectiveness and efficiency of random orthogonalization for FL in massive MIMO.

Ruiquan Huang, Jing Yang, Yingbin Liang

Reward-free reinforcement learning (RF-RL), a recently introduced RL paradigm, relies on random action-taking to explore the unknown environment without any reward feedback information. While the primary goal of the exploration phase in RF-RL is to reduce the uncertainty in the estimated model with minimum number of trajectories, in practice, the agent often needs to abide by certain safety constraint at the same time. It remains unclear how such safe exploration requirement would affect the corresponding sample complexity in order to achieve the desired optimality of the obtained policy in planning. In this work, we make a first attempt to answer this question. In particular, we consider the scenario where a safe baseline policy is known beforehand, and propose a unified Safe reWard-frEe ExploraTion (SWEET) framework. We then particularize the SWEET framework to the tabular and the low-rank MDP settings, and develop algorithms coined Tabular-SWEET and Low-rank-SWEET, respectively. Both algorithms leverage the concavity and continuity of the newly introduced truncated value functions, and are guaranteed to achieve zero constraint violation during exploration with high probability. Furthermore, both algorithms can provably find a near-optimal policy subject to any constraint in the planning phase. Remarkably, the sample complexities under both algorithms match or even outperform the state of the art in their constraint-free counterparts up to some constant factors, proving that safety constraint hardly increases the sample complexity for RF-RL.

Fengyu Gao, Ruiquan Huang, Jing Yang

We study the problems of differentially private federated online prediction from experts against both stochastic adversaries and oblivious adversaries. We aim to minimize the average regret on $m$ clients working in parallel over time horizon $T$ with explicit differential privacy (DP) guarantees. With stochastic adversaries, we propose a Fed-DP-OPE-Stoch algorithm that achieves $\sqrt{m}$-fold speed-up of the per-client regret compared to the single-player counterparts under both pure DP and approximate DP constraints, while maintaining logarithmic communication costs. With oblivious adversaries, we establish non-trivial lower bounds indicating that collaboration among clients does not lead to regret speed-up with general oblivious adversaries. We then consider a special case of the oblivious adversaries setting, where there exists a low-loss expert. We design a new algorithm Fed-SVT and show that it achieves an $m$-fold regret speed-up under both pure DP and approximate DP constraints over the single-player counterparts. Our lower bound indicates that Fed-SVT is nearly optimal up to logarithmic factors. Experiments demonstrate the effectiveness of our proposed algorithms. To the best of our knowledge, this is the first work examining the differentially private online prediction from experts in the federated setting.