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版本更新 · v2arXiv:2611.10188

BiMuon: A Geometry-Aware Stochastic Bilevel Optimization Approach

Zhen Qin, Zhiyao Zhang, Yingbin Liang, Jia Liu

原文摘要

Stochastic bilevel optimization provides a general framework for many machine learning applications, such as hyperparameter learning, data reweighting, language model alignment, and actor-critic reinforcement learning. However, most existing bilevel optimization methods treat matrix-valued gradients as flattened vectors and perform optimization in the resulting vectorized space, ignoring the matrix structures common in modern neural networks. Moreover, the lower-level (LL) problem curvature can induce significant spectral imbalance in the upper-level (UL) geometry. Such limitations of existing bilevel optimization methods motivate us to develop BiMuon, a geometry-aware stochastic bilevel optimization method that integrates implicit hypergradient estimation in bilevel optimization with Muon-style orthogonalized updates at the UL. To our knowledge, BiMuon is the first stochastic BLO method with Muon-style orthogonalized matrix updates and an $O(ε^{-4})$ iteration-complexity guarantee, matching the best-known rates achieved by Muon-type methods based on matrix parameterizations. To improve computational and parallel efficiency for models with multiple matrix parameters, we further study BiMuon for blockwise diagonal matrix approximation and derive a relative stepsize allocation rule based on UL progress and blockwise LL sensitivity. We evaluate BiMuon on representation learning and blockwise bilevel optimization, providing empirical support for our methods.

cs.LG · math.OC

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.10212

DisMUSE: An Efficient Distributed Singular-Spectrum-Based Optimization Approach with Theoretical Convergence Guarantee

Zhen Qin, Zhiyao Zhang, Yingbin Liang, Jia Liu

原文摘要

In recent years, singular-spectrum-based optimizers have attracted increasing attention due to their ability to preserve the matrix structure of neural network gradients, thereby enabling geometry-aware optimization. However, most singular-spectrum-based (SSB) approaches remain centralized, limiting their use in distributed learning infrastructures that exploit massive parallelism. Distributed SSB optimization is still at an early stage, with open questions about convergence guarantees and communication efficiency. To fill this gap, we propose the Distributed Momentum-based Spectral Estimator (DisMUSE), an efficient distributed SSB optimization framework for both data-center and federated settings. Using Muon-style exact orthogonalized momentum as the spectral update, DisMUSE integrates a recursive variance-reduced momentum estimator and achieves an $O((KT)^{-1/3})$ convergence rate, where $K$ and $T$ denote the number of nodes and local iterations per node, respectively. This rate matches the best-known rates for variance-reduced nonconvex distributed optimization. Building on this variance-reduced framework, we study two extensions. First, our DisMUSE method with finite Newton-Schulz (NS) iterations preserves the same convergence order under a uniform normalized support-spectrum condition, up to a multiplicative factor. Second, we develop a communication-efficient variant based on low-rank (LR) momentum transmission and quantify the error it introduces to the stationarity bound, characterizing the trade-off between accuracy and communication cost.

cs.LG · math.OC

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.07069

Finite-Time Convergence and Regret Guarantees for Neural Reinforcement Learning in POMDPs

Jingjuan Huang, Zhiyao Zhang, Alvaro Velasquez, Nathaniel D. Bastian, Jia Liu

原文摘要

Reinforcement learning (RL) in Partially Observable Markov Decision Processes (POMDPs) is computationally challenging due to the curse of long-range dependence on history. Fortunately, recent studies have shown that a range of POMDPs that satisfy the filter stability assumption can be well approximated by a superstate Markov Decision Process (MDP) based on a truncated history in a finite-memory window, with a value gap that decays with the window length. However, existing finite-time convergence analyses on such superstate MDP surrogates are either limited to over-simplified linear function approximation or rely on an i.i.d. sampling oracle that is violated by POMDP trajectories, both of which severely limit the applicability of these theoretical results in practice. This motivates us to bridge the gap by investigating RL in POMDPs with nonlinear neural value function approximation. Our main contributions are threefold: i) We first establish a new finite-state MDP point-wise approximation error bound, which lays the foundation for our RL algorithm design and analysis in POMDPs; ii) By applying Temporal-Difference (TD) learning to POMDP-generated superstate transitions and targeting the Bellman fixed point of the superstate MDP, we prove a finite-time critic error bound with nonlinear neural value function approximation; and iii) By combining the neural critic function approximation error bound with the policy mirror descent framework, we obtain a finite-time sublinear regret against the optimal POMDP value. To the best of our knowledge, such a finite-time sublinear regret based on neural function approximation is the first in the literature for finite-memory POMDPs. Our numerical experiments also verify our theoretical results.

cs.LG · cs.AI

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arXiv ↗PDF ↗