Related papers: Foundations of Multistage Stochastic Programming
A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
A stochastic program typically involves several parameters, including deterministic first-stage parameters and stochastic second-stage elements that serve as input data. These programs are re-solved whenever any input parameter changes.…
Multistage Stochastic Programming (MSP) is a class of models for sequential decision-making under uncertainty. MSP problems are known for their computational intractability due to the sequential nature of the decision-making structure and…
We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…
To tackle the difficulties faced by both stochastic dynamic programming and scenario tree methods, we present some variational approach for numerical solution of stochastic optimal control problems. We consider two different interpretations…
Multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the so-called spectrum of singularities. In this paper we…
Multi-objective optimization models that encode ordered sequential constraints provide a solution to model various challenging problems including encoding preferences, modeling a curriculum, and enforcing measures of safety. A recently…
To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables…
Probabilistic programs with mixed support (both continuous and discrete latent random variables) commonly appear in many probabilistic programming systems (PPSs). However, the existence of the discrete random variables prohibits many basic…
This note summarizes the optimization formulations used in the study of Markov decision processes. We consider both the discounted and undiscounted processes under the standard and the entropy-regularized settings. For each setting, we…
This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
Several attempts to dampen the curse of dimensionnality problem of the Dynamic Programming approach for solving multistage optimization problems have been investigated. One popular way to address this issue is the Stochastic Dual Dynamic…
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…
(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…
Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of…
Most optimization problems in applied sciences realistically involve uncertainty in the parameters defining the cost function, of which only statistical information is known beforehand. In a recent work we introduced a message passing…
Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical…