Related papers: Parameter dependent optimal thresholds, indifferen…
We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…
Necessary conditions of optimality in the form of the Pontryagin Maximum Principle are derived for the Bolza-type discounted problem with free right end. The optimality is understood in the sense of the uniformly overtaking optimality. Such…
We consider the problem of optimal multiple switching in finite horizon, when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem…
Necessary optimality conditions in the form of the maximum principle for control problems with infinite time horizon are considered. Both finite and infinite values of objective functional are allowed since the concept of overtaking or…
The problems of optimally estimating a phase, a direction, and the orientation of a Cartesian frame (or trihedron) with general pure states are addressed. Special emphasis is put on estimation schemes that allow for inconclusive answers or…
We introduce a notion of bounded variation solution for a new class of nonlinear control systems with ordinary and impulsive controls, in which the drift function depends not only on the state, but also on its past history, through a finite…
Let $X$ be a one-dimensional diffusion and let $g\colon[0,T]\times\mathbb{R}\to\mathbb{R}$ be a payoff function depending on time and the value of $X$. The paper analyzes the inverse optimal stopping problem of finding a time-dependent…
This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…
The design of the performance index, also referred to as cost or reward shaping, is central to both optimal control and reinforcement learning, as it directly determines the behaviors, trade-offs, and objectives that the resulting control…
We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…
The standard theory of optimal stopping is based on the idealised assumption that the underlying process is essentially known. In this paper, we drop this restriction and study data-driven optimal stopping for a general diffusion process,…
This work addresses the classic machine learning problem of online prediction with expert advice. A new potential-based framework for the fixed horizon version of this problem has been recently developed using verification arguments from…
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…
This paper is concerned with a discounted optimal control problem of partially observed forward-backward stochastic systems with jumps on infinite horizon. The control domain is convex and a kind of infinite horizon observation equation is…
We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the…
We show that a solution of the optimal assignment problem can be obtained as the limit of the solution of an entropy maximization problem, as a deformation parameter tends to infinity. This allows us to apply entropy maximization algorithms…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
We will investigate the value and inactive region of optimal stopping and one-sided singular control problems by focusing on two fundamental ratios. We shall see that these ratios unambiguously characterize the solution, although usually…
The infinite horizon setting is widely adopted for problems of reinforcement learning (RL). These invariably result in stationary policies that are optimal. In many situations, finite horizon control problems are of interest and for such…
In this paper, Lipschitz univariate constrained global optimization problems where both the objective function and constraints can be multiextremal are considered. The constrained problem is reduced to a discontinuous unconstrained problem…