Solving higher-dimensional continuous-time stochastic control problems by value function regression

Solving optimal control problems by PSO-SVM

The optimal control of problem is about finding a control law for a given system such that a certain optimality criterion is achieved. Methods of solving the optimal control problems are divided into direct methods and mediated methods (through other equations). In this paper, the PSO- SVM indirect method is used to solve a class of optimal control problems. In this paper, we try to determine t...

On adaptive control problems of continuous-time stochastic systems

Let x = (xt)t≥0 be a scalar observed process with control u = (ut)t≥0 described by the stochastic differential equation dxt = θxtdt + utdt + dwt, t ≥ 0, driven by the standard Wiener process (wt)t≥0. Assume the parameter θ to be unknown. The problem solved in this paper is to approximate the process x to the stable Ornstein-Uhlenbeck process x = (xt )t≥0 with the given dynamic parameter a < 0, ...

Stochastic Control in Continuous Time

Learning Continuous Control Policies by Stochastic Value Gradients

We present a unified framework for learning continuous control policies using backpropagation. It supports stochastic control by treating stochasticity in the Bellman equation as a deterministic function of exogenous noise. The product is a spectrum of general policy gradient algorithms that range from model-free methods with value functions to model-based methods without value functions. We us...

Regression methods for stochastic control problems

In this paper we develop several regression algorithms for solving general stochastic optimal control problems via Monte Carlo. This type of algorithms is particulary useful for problems with high-dimensional state space and complex dependence structure of the underlying Markov process with respect to some control. The main idea of the algorithms is to simulate a set of trajectories under some ...