arXiv subjects

Jianting Pan

Publications and source records attributed to Jianting Pan.

6 recordsLinked to original sources

arXiv2026

Relative-Error Composite Federated Optimization with One Server-Side Proximal Step per Round

We consider deterministic composite federated optimization, in which distributed smooth client objectives are combined with a shared, possibly nonsmooth, regularizer. We propose Relative-Error Composite FedDyn (REC-FedDyn), an inexact method that supports partial participation, with one server-side proximal evaluation per communication round. REC-FedDyn employs a directly testable relative-error criterion that allows each client to independently control the accuracy of its local subproblem, without a server-side acceptance test. We establish almost-sure iterate convergence for strongly convex and convex problems, almost-sure asymptotic stationarity for nonconvex problems, and communication and parallel gradient-evaluation complexity bounds, all under partial participation and without assuming bounded data heterogeneity. Experiments on image inpainting, fMRI prediction, and neural-network classification with structured regularization demonstrate efficiency and robustness across levels of data heterogeneity and client participation.

math.OC↗

arXiv2026

Inexact Bregman Sparse Newton Method for Efficient Optimal Transport

Computing exact optimal transport (OT) distances at large scale remains computationally challenging. Entropy-regularized OT can be solved efficiently, but its solution is biased toward the regularized problem, and small regularization parameters often lead to slow convergence and numerical instability. In this paper, we propose \emph{Inexact Bregman Sparse Newton} (IBSN), an efficient method for high-accuracy computation of the original OT problem. Building on a verifiable inexact Bregman proximal framework, IBSN develops a sparse Newton inner solver tailored to the semi-dual formulation, which yields a lower-dimensional Newton system. To accelerate the inner subproblem solves, we introduce a Hessian sparsification strategy tailored to the semi-dual formulation, which reduces the cost of Newton direction computation while preserving key spectral properties. We establish convergence guarantees for the resulting algorithm, including convergence of the inner sparse Newton iterations and global convergence of the overall method to an optimal OT solution. Numerical experiments on synthetic and real datasets show that IBSN is effective in high-accuracy regimes and compares favorably with representative first-order and second-order OT solvers.

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arXiv2026

AdaGamma: State-Dependent Discounting for Temporal Adaptation in Reinforcement Learning

The discount factor in reinforcement learning controls both the effective planning horizon and the strength of bootstrapping, yet most deep RL methods use a single fixed value across all states. State-dependent discounting is a natural way to adapt temporal credit assignment to local state structure, but naively learning a discount function inside deep actor--critic methods creates a self-referential target: the learned discount scales the same bootstrap term against which it is trained. Consequently, TD-error-based objectives can admit a degenerate shortcut, reducing target dependence on downstream value estimates instead of learning meaningful temporal structure. We propose \textbf{AdaGamma}, a practical framework for state-dependent discounting in deep actor--critic reinforcement learning. AdaGamma learns a bounded discount function $γ_ϕ(s)$ and trains it using a return-consistency objective that matches a one-step adaptive bootstrap to a multi-step return computed with a lagged, stop-gradient reference discount. This removes the direct target manipulation path and encourages the discount to encode state-dependent value propagation. We analyze the Bellman operator induced by a fixed state-dependent discount in finite tabular MDPs, proving contraction, exact soft policy iteration, and Lipschitz sensitivity under standard boundedness assumptions. Empirically, AdaGamma integrates into SAC and PPO, avoids TD-collapse, improves continuous-control benchmarks, and achieves statistically significant gains in a four-week online A/B test on the JD Logistics platform.

cs.LG↗

arXiv2026

Newton Method for Fixed-Support Doubly Entropic Wasserstein Barycenter

We study the fixed-support doubly regularized Wasserstein barycenter problem. Using the semi-dual formulation of entropic optimal transport, we reformulate the problem as a smooth, unconstrained, convex optimization problem in the dual variables. We then derive explicit expressions for the gradient and Hessian and develop an exact Newton method for high-accuracy barycenter computation. To improve scalability, we propose a sparse Newton variant that sparsifies the transport probability matrices, thereby reducing the cost of Hessian-vector products. We establish theoretical results for the proposed methods, including Hessian approximation bounds and convergence results. Experiments on synthetic and real datasets show that the sparse Newton method converges faster than

math.OC↗

arXiv2026

Fast projection onto the top-k-sum constraint

This paper develops an efficient algorithm for computing the Euclidean projection onto the top-k-sum constraint, a key operation in financial risk management and matrix optimization problems. Existing projection methods rely on sorting and therefore incur an initial O(nlogn) complexity, which limits their scalability in high-dimensional settings. To address this difficulty, we revisit the Karush-Kuhn-Tucker (KKT) conditions of the projection problem and introduce relaxed conditions that remain sufficient for characterizing the solution. These conditions lead to a simple geometric interpretation: finding the solutions is equivalent to locating the intersection of two monotone piecewise linear functions. Building on this insight, we propose an iterative and highly efficient algorithm that searches directly for the intersection point and completely avoids all sorting procedures. We prove that the algorithm converges globally and reaches the exact solution in a finite number of iterations. Extensive numerical experiments further demonstrate that the proposed algorithm substantially outperforms existing algorithms and exhibits empirical O(n) complexity across a broad range of problem instances.

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arXiv2024

Efficient sparse probability measures recovery via Bregman gradient

This paper presents an algorithm tailored for the efficient recovery of sparse probability measures incorporating $\ell_0$-sparse regularization within the probability simplex constraint. Employing the Bregman proximal gradient method, our algorithm achieves sparsity by explicitly solving underlying subproblems. We rigorously establish the convergence properties of the algorithm, showcasing its capacity to converge to a local minimum with a convergence rate of $O(1/k)$ under mild assumptions. To substantiate the efficacy of our algorithm, we conduct numerical experiments, offering a compelling demonstration of its efficiency in recovering sparse probability measures.

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