Related papers: Partitioned Linear Programming Approximations for …

The definition of factor space and a unified optimization based classification model were developed for linear programming. Intelligent behaviour appeared in a decision process can be treated as a point y, the dynamic state observed and…

Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of…

Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using message-passing algorithms such as belief propagation…

Many large MDPs can be represented compactly using a dynamic Bayesian network. Although the structure of the value function does not retain the structure of the process, recent work has shown that value functions in factored MDPs can often…

We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…

The Augmented Lagrangian Method (ALM) is an iterative method for the solution of equality-constrained non-linear programming problems. In contrast to the quadratic penalty method, the ALM can satisfy equality constraints in an exact way.…

We consider approximate dynamic programming in $\gamma$-discounted Markov decision processes and apply it to approximate planning with linear value-function approximation. Our first contribution is a new variant of Approximate Policy…

We study an approximation method for partially observed Markov decision processes (POMDPs) with continuous spaces. Belief MDP reduction, which has been the standard approach to study POMDPs requires rigorous approximation methods for…

Multi-stage stochastic linear programs (MSLPs) are notoriously hard to solve in general. Linear decision rules (LDRs) yield an approximation of an MSLP by restricting the decisions at each stage to be an affine function of the observed…

Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…

In this paper, we propose a new lower approximation scheme for POMDP with discounted and average cost criterion. The approximating functions are determined by their values at a finite number of belief points, and can be computed efficiently…

Lagrangian relaxation stands among the most efficient approaches for solving a Mixed Integer Linear Programs (MILP) with difficult constraints. Given any duals for these constraints, called Lagrangian Multipliers (LMs), it returns a bound…

We propose a novel randomized linear programming algorithm for approximating the optimal policy of the discounted Markov decision problem. By leveraging the value-policy duality and binary-tree data structures, the algorithm adaptively…

Load balancing and auto scaling are at the core of scalable, contemporary systems, addressing dynamic resource allocation and service rate adjustments in response to workload changes. This paper introduces a novel model and algorithms for…

To overcome the curses of dimensionality and modeling of Dynamic Programming (DP) methods to solve Markov Decision Process (MDP) problems, Reinforcement Learning (RL) methods are adopted in practice. Contrary to traditional RL algorithms…

In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…

We consider partially-specified optimization problems where the goal is to actively, but efficiently, acquire missing information about the problem in order to solve it. An algorithm designer wishes to solve a linear program (LP), $\max…

The load pick-up (LPP) problem searches the optimal configuration of the electrical distribution system (EDS), aiming to minimize the power loss or provide maximum power to the load ends. The piecewise linearization (PWL) approximation…

Large reasoning models (LRMs) achieve higher performance on challenging reasoning tasks by generating more tokens at inference time, but this verbosity often wastes computation on easy problems. Existing solutions, including supervised…

Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…