arXiv subjects

Jianting Pan

Publications and source records attributed to Jianting Pan.

5 recordsLinked to original sources

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

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. While state-dependent discounting is conceptually appealing, naive deep actor--critic implementations can become unstable and degenerate toward TD-error collapse. We propose AdaGamma, a practical deep actor--critic method for state-dependent discounting that learns a state-dependent discount function together with a return-consistency objective to regularize the induced backup structure. On the theory side, we analyze the Bellman operator induced by state-dependent discounting and establish its basic well-posedness properties under suitable conditions. Empirically, AdaGamma integrates into both SAC and PPO, yielding consistent improvements on continuous-control benchmarks, and achieves statistically significant gains in an online A/B test on the JD Logistics platform. These results suggest that state-dependent discounting can be made effective in deep RL when coupled with a return-consistency objective that prevents degenerate target manipulation.

cs.LG↗

arXiv2026

Inexact Bregman Sparse Newton Method for Efficient Optimal Transport

Computing exact Optimal Transport (OT) distances for large-scale datasets is computationally prohibitive. While entropy-regularized alternatives offer speed, they sacrifice precision and frequently suffer from numerical instability in high-accuracy regimes. To address these limitations, we propose the Inexact Bregman Sparse Newton (IBSN) method, which efficiently solves the exact OT problems. Our approach utilizes a Bregman proximal point framework through a sequence of semi-dual subproblems. By solving these subproblems inexactly, we significantly reduce per-iteration complexity while maintaining a theoretical guarantee of convergence to the true optimal plan. To further accelerate the algorithm, we develop a sparse Newton-type solver for the subproblem and employ a Hessian sparsification strategy that drastically lowers memory and time costs without sacrificing accuracy. We provide rigorous theoretical guarantees for the global convergence of the algorithm. Extensive experiments demonstrate that IBSN consistently outperforms state-of-the-art methods in both computational speed and solution precision.

math.OC↗

arXiv2025

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.

math.OC↗

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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