We develop recursive, data-driven, stochastic subgradient methods for optimizing a new,
versatile, and application-driven class of convex risk measures, termed here as mean …

We develop a novel procedure for estimating the optimizer of general convex stochastic
optimization problems of the form min x∈ XE [F (x, ξ)], when the given data is a finite …

The multi-armed bandit (MAB) is a classical model for the exploration vs. exploitation trade-
off. Among existing MAB models, the restless bandit model is of increasing interest because …

In this paper, we study moderate deviations for minimax stochastic programs. We first
establish a minimax delta theorem in large deviations, and then apply the minimax delta …

We motivate and propose a new model for non-cooperative Markov game which considers
the interactions of risk-aware players. This model characterizes the time-consistent dynamic …

In this paper we discuss scenario reduction methods for risk-averse stochastic optimization
problems. Scenario reduction techniques have received some attention in the literature and …

In this paper, we propose a model for non-cooperative Markov games with time-consistent
risk-aware players. In particular, our model characterizes the risk arising from both the …

In this paper, we study asymptotic behaviors of semidefinite programming with a covariance
perturbation. We obtain some moderate deviations, Cramér-type moderate deviations and a …

The area of stochastic optimization (stochastic programming) has gained interests and
attention by its relevance to many problems arising in other areas. The multitude of papers in …

Decision-making is the cognitive process of identifying the decision maker's preference and
finding a corresponding favorite solution. This thesis focus on decision maker's risk …