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This paper presents a new safety specification method that is robust against errors in the probability distribution of disturbances. Our proposed distributionally robust safe policy maximizes the probability of a system remaining in a…
Distributionally robust optimization (DRO) provides a framework for training machine learning models that are able to perform well on a collection of related data distributions (the "uncertainty set"). This is done by solving a min-max…
We study risk-aware linear policy approximations for the optimal operation of an energy system with stochastic wind power, storage, and limited fuel. The resulting problem is a sequential decision-making problem with rolling forecasts. In…
This paper is concerned with the maximum principle of stochastic optimal control problems, where the coefficients of the state equation and the cost functional are uncertain, and the system is generally under Markovian regime switching.…
We consider a classical stochastic control problem in which a diffusion process is controlled by a withdrawal process up to a termination time. The objective is to maximize the expected discounted value of the withdrawals until the…
A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts, or unmodeled temporal effects. We develop and…
We consider a deterministic continuous time model of monopolistic firm, which chooses production and pricing strategies of a single good. Firm's goal is to maximize the discounted profit over infinite time horizon. The no-backlogging…
We study the problem of optimal portfolio selection under stochastic volatility within a continuous time reinforcement learning framework with portfolio constraints. Exploration is modeled through entropy-regularized relaxed controls, where…
Autonomous microgrid planning is a Mixed-Integer Non Convex decision problem that requires to consider investments in both distribution and generation capacity and represents significant computation challenges. We proposed in a previous…
This paper studies the problem of output agreement in networks of nonlinear dynamical systems under time-varying disturbances. Necessary and sufficient conditions for output agreement are derived for the class of incrementally passive…
In this paper we investigate a utility maximization problem with drift uncertainty in a multivariate continuous-time Black-Scholes type financial market which may be incomplete. We impose a constraint on the admissible strategies that…
In this paper, we consider a multistage expected utility maximization problem where the decision maker's utility function at each stage depends on historical data and the information on the true utility function is incomplete. To mitigate…
Reinforcement Learning is a powerful framework for training agents to navigate different situations, but it is susceptible to changes in environmental dynamics. However, solving Markov Decision Processes that are robust to changes is…
A crucial problem in reinforcement learning is learning the optimal policy. We study this in tabular infinite-horizon discounted Markov decision processes under the online setting. The existing algorithms either fail to achieve regret…
The ranking and selection problem is a popular framework in the simulation literature for studying optimal information collection. We study a version of this problem in which the simulation output for each design is normally distributed…
This paper studies the problem of optimal flow control in dynamic inventory systems. A dynamic optimal distribution problem, including time-varying supply and demand, capacity constraints on the transportation lines, and convex flow cost…
This paper considers optimal control problems defined by a monotone dynamical system, a monotone cost, and monotone constraints. We identify families of such problems for which the optimal solution is bang-ride, i.e., always operates on the…
Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we formulate a chance-constrained…
We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by…
Managing insurance and financial risk when data is limited is a key task in the insurance industry. In this paper, we focus on cases where the risk distribution is modeled as a mixture with some components estimable to high precision or…