Deterministic Approximation for Stochastic Control Problems

Deterministic Approximation for Stochastic Control Problems

We consider a class of stochastic control problems where uncertainty is due to driving noises of general nature as well as to rapidly fluctuating processes affecting the drift. We show that, when the noise ”intensity” is small and the fluctuations become fast, the stochastic problems can be approximated by a deterministic one. We also show that the optimal control of the deterministic problem i...

Deep Learning Approximation for Stochastic Control Problems

Many real world stochastic control problems suffer from the “curse of dimensionality”. To overcome this difficulty, we develop a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo sampling. We approximate the time-dependent controls as feedforward neural networks and stack these networks together through model dynamics. The objective fu...

A Deterministic Approach to Stochastic Approximation

Approximation Techniques for Stochastic Combinatorial Optimization Problems

The focus of this thesis is on the design and analysis of algorithms for basic problems in Stochastic Optimization, speciVcally a class of fundamental combinatorial optimization problems where there is some form of uncertainty in the input. Since many interesting optimization problems are computationally intractable (NP-Hard), we resort to designing approximation algorithms which provably outpu...

Approximation algorithms for stochastic scheduling problems

In this dissertation we study a broad class of stochastic scheduling problems characterized by the presence of hard deadline constraints. The input to such a problem is a set of jobs, each with an associated value, processing time, and deadline. We would like to schedule these jobs on a set of machines over time. In our stochastic setting, the processing time of each job is random, known in adv...