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We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…

Risk management often plays an important role in decision making under uncertainty. In quantitative risk management, assessing and optimizing risk metrics requires efficient computing techniques and reliable theoretical guarantees. In this…

Social decision schemes (SDSs) map the voters' preferences over multiple alternatives to a probability distribution over these alternatives. In a seminal result, Gibbard (1977) has characterized the set of SDSs that are strategyproof with…

In the Bayesian approach to sequential decision making, exact calculation of the (subjective) utility is intractable. This extends to most special cases of interest, such as reinforcement learning problems. While utility bounds are known to…

The paper investigates stochastic resource allocation problems with scarce, reusable resources and non-preemtive, time-dependent, interconnected tasks. This approach is a natural generalization of several standard resource management…

Decision-making problems often feature uncertainty stemming from heterogeneous and context-dependent human preferences. To address this, we propose a sequential learning-and-optimization pipeline to learn preference distributions and…

We revisit the problem of portfolio selection, where an investor maximizes utility subject to a risk constraint. Our framework is very general and accommodates a wide range of utility and risk functionals, including non-concave utilities…

We propose a statistically optimal approach to construct data-driven decisions for stochastic optimization problems. Fundamentally, a data-driven decision is simply a function that maps the available training data to a feasible action. It…

In this paper, we study the robust optimal investment and risk control problem for an insurer who owns the insider information about the financial market and the insurance market under model uncertainty. Both financial risky asset process…

In this paper we propose a framework towards achieving two intertwined objectives: (i) equipping reinforcement learning with active exploration and deliberate information gathering, such that it regulates state and parameter uncertainties…

Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues…

In this paper the utility optimization problem for a general insurance model is studied. The reserve process of the insurance company is described by a stochastic differential equation driven by a Brownian motion and a Poisson random…

Policy evaluation with linear function approximation is an important problem in reinforcement learning. When facing high-dimensional feature spaces, such a problem becomes extremely hard considering the computation efficiency and quality of…

This paper addresses the portfolio selection problem for nonlinear law-dependent preferences in continuous time, which inherently exhibit time inconsistency. Employing the method of stochastic maximum principle, we establish verification…

We investigate the problem of synthesizing distributionally robust control policies for stochastic systems under safety and reach-avoid specifications. Using a game-theoretical framework, we consider the setting where the probability…

Stochastic games are often used to model reactive processes. We consider the problem of synthesizing an optimal almost-sure winning strategy in a two-player (namely a system and its environment) turn-based stochastic game with both a…

This paper introduces a novel test for conditional stochastic dominance (CSD) at specific values of the conditioning covariates, referred to as target points. The test is relevant for analyzing income inequality, evaluating treatment…

This paper establishes non-asymptotic convergence of the cutoffs in Random serial dictatorship in an environment with many students, many schools, and arbitrary student preferences. Convergence is shown to hold when the number of schools,…

We study to what extent may stochastic gradient descent (SGD) be understood as a "conventional" learning rule that achieves generalization performance by obtaining a good fit to training data. We consider the fundamental stochastic convex…

In this paper, we consider the problem of learning safe policies for probabilistic-constrained reinforcement learning (RL). Specifically, a safe policy or controller is one that, with high probability, maintains the trajectory of the agent…