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Related papers: Dual formulation of second order target problems

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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

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…

Probability · Mathematics 2021-04-13 Suryadeepto Nag

We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (2019), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under…

Probability · Mathematics 2020-01-09 Bruno Bouchard , Xiaolu Tan

Multistage stochastic optimization problems are oftentimes formulated informally in a pathwise way. These are correct in a discrete setting and suitable when addressing computational challenges, for example. But the pathwise problem…

Optimization and Control · Mathematics 2021-02-23 Paul Dommel , Alois Pichler

We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…

Probability · Mathematics 2016-06-28 Fulvia Confortola , Marco Fuhrman , Jean Jacod

We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a…

Optimization and Control · Mathematics 2020-08-24 Andrzej Ruszczynski , Jianing Yao

A splitting scheme for backward doubly stochastic differential equations is proposed. The main idea is to decompose a backward doubly stochastic differential equation into a backward stochastic differential equation and a stochastic…

Numerical Analysis · Mathematics 2021-03-17 Feng Bao , Yanzhao Cao , He Zhang

This paper presents a mathematical framework for causal nonlinear prediction in settings where observations are generated from an underlying hidden Markov model (HMM). Both the problem formulation and the proposed solution are motivated by…

Machine Learning · Computer Science 2026-03-16 Heng-Sheng Chang , Prashant G. Mehta

This paper is concerned with the development and use of duality theory for a nonlinear filtering model with white noise observations. The main contribution of this paper is to introduce a stochastic optimal control problem as a dual to the…

Optimization and Control · Mathematics 2022-08-16 Jin Won Kim , Prashant G. Mehta

In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…

Optimization and Control · Mathematics 2025-04-08 Prashant Khanduri , Ioannis Tsaknakis , Yihua Zhang , Sijia Liu , Mingyi Hong

We develop dual approaches for continuous-time stochastic control problems, enabling the computation of robust dual bounds in high-dimensional state and control spaces. Building on the dual formulation proposed in [L. C. G. Rogers, SIAM…

Optimization and Control · Mathematics 2026-04-10 Mathieu Laurière , Jiefei Yang

In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the…

Optimization and Control · Mathematics 2023-11-08 Tommaso Giovannelli , Griffin Dean Kent , Luis Nunes Vicente

We propose a novel reformulation of the stochastic optimal control problem as an approximate inference problem, demonstrating, that such a interpretation leads to new practical methods for the original problem. In particular we characterise…

Machine Learning · Computer Science 2010-09-22 Konrad Rawlik , Marc Toussaint , Sethu Vijayakumar

This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…

Probability · Mathematics 2022-05-26 Jian Song , Meng Wang

This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex…

Optimization and Control · Mathematics 2022-06-01 Teemu Pennanen , Ari-Pekka Perkkiö

We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by `controlled' Markov noise. In particular, both the faster and slower recursions have non-additive controlled Markov noise…

Dynamical Systems · Mathematics 2017-02-28 Prasenjit Karmakar , Shalabh Bhatnagar

This article studies convex duality in stochastic optimization over finite discrete-time. The first part of the paper gives general conditions that yield explicit expressions for the dual objective in many applications in operations…

Optimization and Control · Mathematics 2015-04-28 Sara Biagini , Teemu Pennanen , Ari-Pekka Perkkiö

In this paper a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for…

Probability · Mathematics 2009-09-29 Brahim Boufoussi , Jan Van Casteren , N. Mrhardy

This paper deals with the problem of estimating second-order parameter sensitivities for stochastic reaction networks, where the reaction dynamics is modeled as a continuous time Markov chain over a discrete state space. Estimation of such…

Probability · Mathematics 2014-07-29 Ankit Gupta , Mustafa Khammash

We study a class of second order variational inequalities with bilateral constraints. Under certain conditions we show the existence of a unique viscosity solution of these variational inequalities and give a stochastic representation to…

Analysis of PDEs · Mathematics 2007-05-23 Mrinal K Ghosh , K S Mallikarjuna Rao