Related papers: On the correctness of monadic backward induction

We consider stochastic strongly-convex-strongly-concave (SCSC) saddle point (SP) problems which frequently arise in applications ranging from distributionally robust learning to game theory and fairness in machine learning. We focus on the…

We propose novel classical and quantum online algorithms for learning finite-horizon and infinite-horizon average-reward Markov Decision Processes (MDPs). Our algorithms are based on a hybrid exploration-generative reinforcement learning…

In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…

In this contribution, we augment the metric learning setting by introducing a parametric pseudo-distance, trained jointly with the encoder. Several interpretations are thus drawn for the learned distance-like model's output. We first show…

Multi-environment POMDPs (ME-POMDPs) extend standard POMDPs with discrete model uncertainty. ME-POMDPs represent a finite set of POMDPs that share the same state, action, and observation spaces, but may arbitrarily vary in their transition,…

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state…

An adaptive controller is proposed and analyzed for the class of infinite-horizon optimal control problems in positive linear systems presented in (Ohlin et al., 2024b). This controller is derived from the solution of a "data-driven…

Reinforcement learning is widely used in applications where one needs to perform sequential decisions while interacting with the environment. The problem becomes more challenging when the decision requirement includes satisfying some safety…

We propose an interior point method (IPM) for solving semidefinite programming problems (SDPs). The standard interior point algorithms used to solve SDPs work in the space of positive semidefinite matrices. Contrary to that the proposed…

This paper presents exact Semi-Definite Program (SDP) reformulations for infinite-dimensional moment optimization problems involving a new class of piecewise Sum-of-Squares (SOS)-convex functions and projected spectrahedral support sets.…

We show {\it semidefinite programming} (SDP) feasibility problem is equivalent to solving a {\it convex hull relaxation} (CHR) for a finite system of quadratic equations. On the one hand, this offers a simple description of SDP. On the…

We present a finite-horizon optimization algorithm that extends the established concept of Dual Dynamic Programming (DDP) in two ways. First, in contrast to the linear costs, dynamics, and constraints of standard DDP, we consider problems…

Differential Dynamic Programming (DDP) is an efficient computational tool for solving nonlinear optimal control problems. It was originally designed as a single shooting method and thus is sensitive to the initial guess supplied. This work…

Neural networks are central to many emerging technologies, but verifying their correctness remains a major challenge. It is known that network outputs can be sensitive and fragile to even small input perturbations, thereby increasing the…

In this paper, we will develop a systematic approach to deriving guaranteed bounds for approximate dynamic programming (ADP) schemes in optimal control problems. Our approach is inspired by our recent results on bounding the performance of…

This paper proposes a general semantic framework for verifying programs with arbitrary monadic side-effects using Dijkstra monads, which we define as monad-like structures indexed by a specification monad. We prove that any monad morphism…

We introduce an extension of Dual Dynamic Programming (DDP) to solve convex nonlinear dynamic programming equations. We call Inexact DDP (IDDP) this extension which applies to situations where some or all primal and dual subproblems to be…

High-index saddle dynamics (HiSD) is an effective approach for computing saddle points of a prescribed Morse index and constructing solution landscapes for complex nonlinear systems. However, for problems with ill-conditioned Hessians…

We consider impulse control of stochastic functional differential equations (SFDEs) driven by L\'evy processes under an additional $L^p$-Lipschitz condition on the coefficients. Our results, which are first derived for a general stochastic…

For a real valued function, a point is critical if its derivatives are zero, and a critical point is a saddle point if it is not a local extrema. In this paper, we study algorithms to find saddle points of general Morse index. Our approach…