Related papers: RL-SPH: Learning to Achieve Feasible Solutions for…

Flexibility design problems are a class of problems that appear in strategic decision-making across industries, where the objective is to design a ($e.g.$, manufacturing) network that affords flexibility and adaptivity. The underlying…

Scheduling on dataflow graphs (also known as computation graphs) is an NP-hard problem. The traditional exact methods are limited by runtime complexity, while reinforcement learning (RL) and heuristic-based approaches struggle with…

Induction benefits from useful priors. Penalized regression approaches, like ridge regression, shrink weights toward zero but zero association is usually not a sensible prior. Inspired by simple and robust decision heuristics humans use, we…

We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FO-definable class of graphs. For each solution there may be many graphs representing it.…

We study the problem of detecting infeasibility of large-scale linear programming problems using the primal-dual hybrid gradient method (PDHG) of Chambolle and Pock (2011). The literature on PDHG has mostly focused on settings where the…

Many traditional algorithms for solving combinatorial optimization problems involve using hand-crafted heuristics that sequentially construct a solution. Such heuristics are designed by domain experts and may often be suboptimal due to the…

A significant challenge for the practical application of reinforcement learning in the real world is the need to specify an oracle reward function that correctly defines a task. Inverse reinforcement learning (IRL) seeks to avoid this…

With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmic-barrier problems of nonlinear programs. As a result, a two-parameter primal-dual nonlinear system is…

Large Language Models (LLMs) often struggle with problems that require multi-step reasoning. For small-scale open-source models, Reinforcement Learning with Verifiable Rewards (RLVR) fails when correct solutions are rarely sampled even…

The integration of Reinforcement Learning (RL) with heuristic methods is an emerging trend for solving optimization problems, which leverages RL's ability to learn from the data generated during the search process. One promising approach is…

In this paper, we analyze the recently proposed stochastic primal-dual hybrid gradient (SPDHG) algorithm and provide new theoretical results. In particular, we prove almost sure convergence of the iterates to a solution with convexity and…

The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike those obtained in most splitting methods, these subproblems…

Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents a significant computational challenge, motivating the development of machine learning-based…

Recent advances have demonstrated the effectiveness of Reinforcement Learning (RL) in improving the reasoning capabilities of Large Language Models (LLMs). However, existing works inevitably rely on high-quality instructions and verifiable…

In this paper we propose a class of randomized primal-dual methods to contend with large-scale saddle point problems defined by a convex-concave function $\mathcal{L}(\mathbf{x},y)\triangleq\sum_{i=1}^m f_i(x_i)+\Phi(\mathbf{x},y)-h(y)$. We…

Large-scale LP problems from industry usually contain much redundancy that severely hurts the efficiency and reliability of solving LPs, making presolve (i.e., the problem simplification module) one of the most critical components in modern…

We introduce DeepPSL a variant of probabilistic soft logic (PSL) to produce an end-to-end trainable system that integrates reasoning and perception. PSL represents first-order logic in terms of a convex graphical model -- hinge-loss Markov…

Reinforcement Learning from Human Feedback (RLHF) aligns Large Language Models (LLMs) with human preferences, yet the underlying reward signals they internalize remain hidden, posing a critical challenge for interpretability and safety.…

Reinforcement learning with verifiable rewards (RLVR) has achieved remarkable success in enhancing the reasoning capabilities of large language models (LLMs). However, existing RLVR methods often suffer from exploration inefficiency due to…

We investigate the use of low-precision first-order methods (FOMs) within a fix-and-propagate (FP) framework for solving mixed-integer programming problems (MIPs). We employ GPU-accelerated PDLP, a variant of the Primal-Dual Hybrid Gradient…