Related papers: On Partial Opimality by Auxiliary Submodular Probl…

Sequential optimality conditions play an important role in constrained optimization since they provide necessary conditions without requiring constraint qualifications (CQs). This paper introduces a second-order extension of the Approximate…

Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…

Double Machine Learning is often justified by nuisance-rate conditions, yet finite-sample reliability also depends on the conditioning of the orthogonal-score Jacobian. This conditioning is typically assumed rather than tracked. When…

We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…

We introduce the problem of minimal actuator placement in a linear control system so that a bound on the minimum control effort for a given state transfer is satisfied while controllability is ensured. We first show that this is an NP-hard…

Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…

Many computer vision problems require optimization of binary non-submodular energies. We propose a general optimization framework based on local submodular approximations (LSA). Unlike standard LP relaxation methods that linearize the whole…

This papers deals with the constrained discounted control of piecewise deterministic Markov process (PDMPs) in general Borel spaces. The control variable acts on the jump rate and transition measure, and the goal is to minimize the total…

Karger used spanning tree packings to derive a near linear-time randomized algorithm for the global minimum cut problem as well as a bound on the number of approximate minimum cuts. This is a different approach from his well-known random…

In current model-free reinforcement learning (RL) algorithms, stability criteria based on sampling methods are commonly utilized to guide policy optimization. However, these criteria only guarantee the infinite-time convergence of the…

Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…

We propose a novel spatially continuous framework for convex relaxations based on functional lifting. Our method can be interpreted as a sublabel-accurate solution to multilabel problems. We show that previously proposed functional lifting…

We study relaxations for linear programs with complementarity constraints, especially instances whose complementary pairs of variables are not independent. Our formulation is based on identifying vertex covers of the conflict graph of the…

We consider the problem of controlling a fully specified Markov decision process (MDP), also known as the planning problem, when the state space is very large and calculating the optimal policy is intractable. Instead, we pursue the more…

Off-policy problems such as policy staleness and training--inference mismatch have become a major bottleneck for training stability and further exploration in LLM RL. The distribution gap between the inference and updated policies grows…

Constrained partially observable Markov decision processes (CPOMDPs) have been used to model various real-world phenomena. However, they are notoriously difficult to solve to optimality, and there exist only a few approximation methods for…

Interval Markov decision processes are a class of Markov models where the transition probabilities between the states belong to intervals. In this paper, we study the problem of efficient estimation of the optimal policies in Interval…

The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…

The demand for classical-quantum hybrid algorithms to solve large-scale combinatorial optimization problems using quantum annealing (QA) has increased. One approach involves obtaining an approximate solution using classical algorithms and…

Many reinforcement learning algorithms can be seen as versions of approximate policy iteration (API). While standard API often performs poorly, it has been shown that learning can be stabilized by regularizing each policy update by the…