English
Related papers

Related papers: Augmented Lagrangian Method for Last-Iterate Conve…

200 papers

The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual…

Optimization and Control · Mathematics 2022-10-21 Egor Gladin , Maksim Lavrik-Karmazin , Karina Zainullina , Varvara Rudenko , Alexander Gasnikov , Martin Takáč

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…

Optimization and Control · Mathematics 2012-10-10 Manya V. Afonso , José M. Bioucas-Dias , Mário A. T. Figueiredo

This paper considers the problem of finding near-optimal Markovian randomized (MR) policies for finite-state-action, infinite-horizon, constrained risk-sensitive Markov decision processes (CRSMDPs). Constraints are in the form of standard…

Optimization and Control · Mathematics 2023-03-14 Uday Kumar M , Sanjay P Bhat , Veeraruna Kavitha , Nandyala Hemachandra

We study the optimization of the expected long-term reward in finite partially observable Markov decision processes over the set of stationary stochastic policies. In the case of deterministic observations, also known as state aggregation,…

Optimization and Control · Mathematics 2022-11-18 Mareike Dressler , Marina Garrote-López , Guido Montúfar , Johannes Müller , Kemal Rose

We study the problem of learning policy of an infinite-horizon, discounted cost, Markov decision process (MDP) with a large number of states. We compute the actions of a policy that is nearly as good as a policy chosen by a suitable oracle…

Machine Learning · Computer Science 2019-09-02 Masoud Badiei Khuzani , Varun Vasudevan , Hongyi Ren , Lei Xing

We analyze the last-iterate convergence of the Anchored Gradient Descent Ascent algorithm for smooth convex-concave min-max problems. While previous work established a last-iterate rate of $\mathcal{O}(1/t^{2-2p})$ for the squared gradient…

We study the policy testing problem in discounted Markov decision processes (MDPs) in the fixed-confidence setting under a generative model with static sampling. The goal is to decide whether the value of a given policy exceeds a specified…

Machine Learning · Statistics 2026-04-21 Kaito Ariu , Po-An Wang , Alexandre Proutiere , Kenshi Abe

Markov decision processes (MDPs) with large number of states are of high practical interest. However, conventional algorithms to solve MDP are computationally infeasible in this scenario. Approximate dynamic programming (ADP) methods tackle…

Systems and Control · Computer Science 2014-11-19 Chandrashekar Lakshminarayanan , Shalabh Bhatnagar

Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…

Optimization and Control · Mathematics 2025-05-20 Viktoriya Nikitina , Alberto De Marchi , Matthias Gerdts

The ability to compute reward-optimal policies for given and known finite Markov decision processes (MDPs) underpins a variety of applications across planning, controller synthesis, and verification. However, we often want policies (1) to…

Logic in Computer Science · Computer Science 2025-11-18 Linus Heck , Filip Macák , Milan Češka , Sebastian Junges

Generalized nonlinear programming is considered without any convexity assumption, capturing a variety of problems that include nonsmooth objectives, combinatorial structures, and set-membership nonlinear constraints. We extend the augmented…

Optimization and Control · Mathematics 2024-04-02 Alberto De Marchi

In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on…

Optimization and Control · Mathematics 2018-09-12 Marianna De Santis , Franz Rendl , Angelika Wiegele

We consider approximate dynamic programming for the infinite-horizon stationary $\gamma$-discounted optimal control problem formalized by Markov Decision Processes. While in the exact case it is known that there always exists an optimal…

Optimization and Control · Mathematics 2013-04-23 Boris Lesner , Bruno Scherrer

We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…

Optimization and Control · Mathematics 2019-08-09 Brian Dandurand , Natashia Boland , Jeffrey Christiansen , Andrew Eberhard , Fabricio Oliveira

In this paper we propose and analyze inexact and stochastic versions of the CGALP algorithm developed in the authors' previous paper, which we denote ICGALP, that allows for errors in the computation of several important quantities. In…

Optimization and Control · Mathematics 2022-10-20 Antonio Silveti-Falls , Cesare Molinari , Jalal Fadili

In this paper, we develop a unified framework able to certify both exponential and subexponential convergence rates for a wide range of iterative first-order optimization algorithms. To this end, we construct a family of parameter-dependent…

Optimization and Control · Mathematics 2018-02-26 Mahyar Fazlyab , Alejandro Ribeiro , Manfred Morari , Victor M. Preciado

We analyze the convergence behaviour of a recently proposed algorithm for regularized estimation called Dual Augmented Lagrangian (DAL). Our analysis is based on a new interpretation of DAL as a proximal minimization algorithm. We…

Machine Learning · Statistics 2011-06-07 Ryota Tomioka , Taiji Suzuki , Masashi Sugiyama

The mathematical framework of hybrid system is a recent and general tool to treat control systems involving control action of heterogeneous nature. In this paper, we construct and test a semi-Lagrangian numerical scheme for solving the…

Numerical Analysis · Mathematics 2016-08-03 Roberto Ferretti , Achille Sassi

We introduce a twice differentiable augmented Lagrangian for nonlinear optimization with general inequality constraints and show that a strict local minimizer of the original problem is an approximate strict local solution of the augmented…

Optimization and Control · Mathematics 2021-06-30 Xin-Wei Liu , Yu-Hong Dai , Ya-Kui Huang , Jie Sun

We study the problem of infinite-horizon average-reward reinforcement learning with linear Markov decision processes (MDPs). The associated Bellman operator of the problem not being a contraction makes the algorithm design challenging.…

Machine Learning · Statistics 2025-03-12 Kihyuk Hong , Woojin Chae , Yufan Zhang , Dabeen Lee , Ambuj Tewari