Related papers: Efficient Stochastic Optimal Control through Appro…
We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form…
Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to act only when confident and abstain when uncertainty is high. Given a target accuracy, our goal is to minimize…
Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…
Bayesian optimization is a sample-efficient method for solving expensive, black-box optimization problems. Stochastic programming concerns optimization under uncertainty where, typically, average performance is the quantity of interest. In…
Traditional statistical estimation, or statistical inference in general, is static, in the sense that the estimate of the quantity of interest does not change the future evolution of the quantity. In some sequential estimation problems…
We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel…
Bayesian inference is an effective approach for solving statistical learning problems especially with uncertainty and incompleteness. However, inference efficiencies are physically limited by the bottlenecks of conventional computing…
Affine policies (or control) are widely used as a solution approach in dynamic optimization where computing an optimal adjustable solution is usually intractable. While the worst case performance of affine policies can be significantly bad,…
In this paper we present a novel sampling-based numerical scheme designed to solve a certain class of stochastic optimal control problems, utilizing forward and backward stochastic differential equations (FBSDEs). By means of a nonlinear…
Motivated by emerging applications in machine learning, we consider an optimization problem in a general form where the gradient of the objective function is available through a biased stochastic oracle. We assume a bias-control parameter…
In this note, we consider the existence and uniqueness of the solution of a time-dependent optimal control problem constrained by a partial differential equation with uncertain inputs. Relying on the Lions' Lemma for deterministic problems,…
When the underlying probability distribution in a stochastic optimization is observed only through data, various data-driven formulations have been studied to obtain approximate optimal solutions. We show that no such formulations can, in a…
Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is…
This paper presents a strictly convex chance-constrained stochastic control framework that accounts for uncertainty in control specifications such as reference trajectories and operational constraints. By jointly optimizing control inputs…
In this article, we consider a stochastic linear quadratic control problem with partial observation. A near optimal control in the weak formulation is characterized. The main features of this paper are the presence of the control in the…
We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assumptions on the dynamics and the costs are rather general and…
Approximate inference in complex probabilistic models such as deep Gaussian processes requires the optimisation of doubly stochastic objective functions. These objectives incorporate randomness both from mini-batch subsampling of the data…
This study proposes a method for designing stabilizing suboptimal controllers for nonlinear stochastic systems. These systems include time-invariant stochastic parameters that represent uncertainty of dynamics, posing two key difficulties…