Related papers: EM Algorithm and Stochastic Control in Economics
Many techniques originally developed in the context of deterministic control theory have been recently applied to the quest for optimal protocols in stochastic processes. Given a system subject to environmental fluctuations, one may ask…
This paper focuses on stochastic optimal control problems with constraints in law, which are rewritten as optimization (minimization) of probability measures problem on the canonical space. We introduce a penalized version of this type of…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
We consider a stochastic linear system and address the design of a finite horizon control policy that is optimal according to some average cost criterion and accounts also for probabilistic constraints on both the input and state variables.…
Finite mixture models are powerful tools for modelling and analyzing heterogeneous data. Parameter estimation is typically carried out using maximum likelihood estimation via the Expectation-Maximization (EM) algorithm. Recently, the…
This paper concerns discrete-time infinite-horizon stochastic control systems with Borel state and action spaces and universally measurable policies. We study optimization problems on strategic measures induced by the policies in these…
We use classical tools from calculus of variations to formally derive necessary conditions for a Markov control to be optimal in a standard finite time horizon stochastic control problem. As an example, we solve the well-known Merton…
We study a maturity randomization technique for approximating optimal control problems. The algorithm is based on a sequence of control problems with random terminal horizon which converges to the original one. This is a generalization of…
Many modern computational approaches to classical problems in quantitative finance are formulated as empirical loss minimization (ERM), allowing direct applications of classical results from statistical machine learning. These methods,…
This paper introduces a new formulation for stochastic optimal control and stochastic dynamic optimization that ensures safety with respect to state and control constraints. The proposed methodology brings together concepts such as…
We study optimization for losses that admit a variance-mean scale-mixture representation. Under this representation, each EM iteration is a weighted least squares update in which latent variables determine observation and parameter weights;…
Latent variable models are a fundamental modeling tool in machine learning applications, but they present significant computational and analytical challenges. The popular EM algorithm and its variants, is a much used algorithmic tool; yet…
We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an $N$-particle…
We present the Stochastic alternate Linearization Method (StochaLM), a token-based method for distributed optimization. This algorithm finds the solution of a consensus optimization problem by solving a sequence of subproblems where some…
As opposed to stabilizing to a reference trajectory or state, Economic Model Predictive Control (EMPC) optimizes economic performance over a prediction horizon, making it particularly attractive for economic microgrid (MG) dispatch.…
(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative…
The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…
In this paper, we propose an original approach to stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probability measures. We then introduce a penalized…
This study presents a comprehensive approach to optimizing inventory management under stochastic demand by leveraging Monte Carlo Simulation (MCS) with grid search and Bayesian optimization. By using a business case of historical demand…
This paper proposes a real-time model predictive control (MPC) scheme to execute multiple tasks using robots over a finite-time horizon. In industrial robotic applications, we must carefully consider multiple constraints for avoiding joint…