Shaofu Yang

Luyao Guo, Xinli Shi, Shaofu Yang et al.

In this paper, we propose a novel Dual Inexact Splitting Algorithm (DISA) for distributed convex composite optimization problems, where the local loss function consists of a smooth term and a possibly nonsmooth term composed with a linear mapping. DISA, for the first time, eliminates the dependence of the convergent step-size range on the Euclidean norm of the linear mapping, while inheriting the advantages of the classic Primal-Dual Proximal Splitting Algorithm (PD-PSA): simple structure and easy implementation. This indicates that DISA can be executed without prior knowledge of the norm, and tiny step-sizes can be avoided when the norm is large. Additionally, we prove sublinear and linear convergence rates of DISA under general convexity and metric subregularity, respectively. Moreover, we provide a variant of DISA with approximate proximal mapping and prove its global convergence and sublinear convergence rate. Numerical experiments corroborate our theoretical analyses and demonstrate a significant acceleration of DISA compared to existing PD-PSAs.

Luyao Guo, Jinde Cao, Xinli Shi et al.

In this paper, we propose a novel primal-dual proximal splitting algorithm (PD-PSA), named BALPA, for the composite optimization problem with equality constraints, where the loss function consists of a smooth term and a nonsmooth term composed with a linear mapping. In BALPA, the dual update is designed as a proximal point for a time-varying quadratic function, which balances the implementation of primal and dual update and retains the proximity-induced feature of classic PD-PSAs. In addition, by this balance, BALPA eliminates the inefficiency of classic PD-PSAs for composite optimization problems in which the Euclidean norm of the linear mapping or the equality constraint mapping is large. Therefore, BALPA not only inherits the advantages of simple structure and easy implementation of classic PD-PSAs but also ensures a fast convergence when these norms are large. Moreover, we propose a stochastic version of BALPA (S-BALPA) and apply the developed BALPA to distributed optimization to devise a new distributed optimization algorithm. Furthermore, a comprehensive convergence analysis for BALPA and S-BALPA is conducted, respectively. Finally, numerical experiments demonstrate the efficiency of the proposed algorithms.

Xinglin Zhou, Yifu Yuan, Shaofu Yang et al.

Hierarchical reinforcement learning (HRL) provides a promising solution for complex tasks with sparse rewards of intelligent agents, which uses a hierarchical framework that divides tasks into subgoals and completes them sequentially. However, current methods struggle to find suitable subgoals for ensuring a stable learning process. Without additional guidance, it is impractical to rely solely on exploration or heuristics methods to determine subgoals in a large goal space. To address the issue, We propose a general hierarchical reinforcement learning framework incorporating human feedback and dynamic distance constraints (MENTOR). MENTOR acts as a "mentor", incorporating human feedback into high-level policy learning, to find better subgoals. As for low-level policy, MENTOR designs a dual policy for exploration-exploitation decoupling respectively to stabilize the training. Furthermore, although humans can simply break down tasks into subgoals to guide the right learning direction, subgoals that are too difficult or too easy can still hinder downstream learning efficiency. We propose the Dynamic Distance Constraint (DDC) mechanism dynamically adjusting the space of optional subgoals. Thus MENTOR can generate subgoals matching the low-level policy learning process from easy to hard. Extensive experiments demonstrate that MENTOR uses a small amount of human feedback to achieve significant improvement in complex tasks with sparse rewards.

Cheng Sun, Zhen Zhang, Shaofu Yang

In this paper, we study a second-order approach to policy optimization in reinforcement learning. Existing second-order methods often suffer from suboptimal sample complexity or rely on unrealistic assumptions about importance sampling. To overcome these limitations, we propose VR-CR-PN, a variance-reduced cubic-regularized policy Newton algorithm. To the best of our knowledge, this is the first algorithm that integrates Hessian-aided variance reduction with second-order policy optimization, effectively addressing the distribution shift problem and achieving best-known sample complexity under general nonconvex conditions but without the need for importance sampling. We theoretically establish that VR-CR-PN achieves a sample complexity of $\tilde{\mathcal{O}}(ε^{-3})$ to reach an $ε$-second-order stationary point, significantly improving upon the previous best result of $\tilde{\mathcal{O}}(ε^{-3.5})$ under comparable assumptions. As an additional contribution, we introduce a novel Hessian estimator for the expected return function, which admits a uniform upper bound independent of the horizon length $H$, allowing the algorithm to achieve horizon-independent sample complexity.