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Decision-making problems of sequential nature, where decisions made in the past may have an impact on the future, are used to model many practically important applications. In some real-world applications, feedback about a decision is…
In this article we prove new results regarding the existence and the uniqueness of global variational solutions to Neumann initial-boundary value problems for a class of non-autonomous stochastic parabolic partial differential equations.…
We consider a discounted infinite horizon optimal stopping problem. If the underlying distribution is known a priori, the solution of this problem is obtained via dynamic programming (DP) and is given by a well known threshold rule. When…
We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…
We study how a platform should design early exposure and rewards when creators strategically choose quality before release. A short testing window with a pass/fail bar induces a pass probability, the slope of which is the key sufficient…
The primitive equations for geophysical flows are studied under the influence of {\em stochastic wind driven boundary conditions} modeled by a cylindrical Wiener process. We adapt an approach by Da Prato and Zabczyk for stochastic boundary…
In this paper we study a ratio-dependent predator-prey model with a free boundary causing by both prey and predator over a one dimensional habitat. We study the long time behaviors of the two species and prove a spreading-vanishing…
We give a memoryless scale-invariant randomized algorithm for the Buffer Management with Bounded Delay problem that is e/(e-1)-competitive against an adaptive adversary, together with better performance guarantees for many restricted…
For job scheduling systems, where jobs require some amount of processing and then leave the system, it is natural for each user to provide an estimate of their job's time requirement in order to aid the scheduler. However, if there is no…
We consider impulse control problems in finite horizon for diffusions with decision lag and execution delay. The new feature is that our general framework deals with the important case when several consecutive orders may be decided before…
Joint detection and estimation refers to deciding between two or more hypotheses and, depending on the test outcome, simultaneously estimating the unknown parameters of the underlying distribution. This problem is investigated in a…
In this paper we propose a novel semi-definite programming approach that solves reach-avoid problems over open (i.e., not bounded a priori) time horizons for dynamical systems modeled by polynomial stochastic differential equations. The…
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…
Information-directed sampling (IDS) is a powerful framework for solving bandit problems which has shown strong results in both Bayesian and frequentist settings. However, frequentist IDS, like many other bandit algorithms, requires that one…
The path planning problem for autonomous exploration of an unknown region by a robotic agent typically employs frontier-based or information-theoretic heuristics. Frontier-based heuristics typically evaluate the information gain of a…
Boundary prediction in images as well as video has been a very active topic of research and organizing visual information into boundaries and segments is believed to be a corner stone of visual perception. While prior work has focused on…
Delayed outcomes are ubiquitous in online experimentation. When such a temporal dimension is present, treatment influences not only the outcome value but also the outcome timing, which can move in opposite directions. Motivated by the…
This work deals with the problem of choosing a time step for the numerical solution of boundary value problems for parabolic equations. The problem solution is derived using the fully implicit scheme, whereas a time step is selected via…
This paper studies a risk-sensitive decision-making problem under uncertainty. It considers a decision-making process that unfolds over a fixed number of stages, in which a decision-maker chooses among multiple alternatives, some of which…
Reward models (RMs) are essential for aligning large language models (LLM) with human expectations. However, existing RMs struggle to capture the stochastic and uncertain nature of human preferences and fail to assess the reliability of…