Session: Advances in Data-driven Optimization
Chair: Rui Gao & Daniel Kuhn
Cluster: Optimization Under Uncertainty and Data-driven Optimization
Talk 1: A Class of Interpretable and Decomposable Multi-period Convex Risk Measures
Speaker: Luhao Zhang
Abstract: Multi-period risk measures evaluate the risk of a stochastic process by assigning it a scalar value. A desirable property of these measures is dynamic decomposition, which allows the risk evaluation to be expressed as a dynamic program. However, many widely used risk measures, such as Conditional Value-at-Risk, do not possess this property. In this work, we introduce a novel class of multi-period convex risk measures that do admit dynamic decomposition. Our proposed risk measure evaluates the worst-case expectation of a random outcome across all possible stochastic processes, penalized by their deviations from a nominal process in terms of both the likelihood ratio and the outcome. We show that this risk measure can be reformulated as a dynamic program, where, at each time period, it assesses the worst-case expectation of future costs, adjusting by reweighting and relocating the conditional nominal distribution. This recursive structure enables more efficient computation and clearer interpretation of risk over multiple periods.
Talk 2: An MILP-Based Solution Scheme for Factored and Robust Factored Markov Decision Processes
Speaker: Man-Chung Yue
Abstract: Factored Markov decision processes (MDPs) are a prominent paradigm within the artificial intelligence community for modeling and solving large-scale MDPs whose rewards and dynamics decompose into smaller, loosely interacting components. Through the use of dynamic Bayesian networks and context-specific independence, factored MDPs can achieve an exponential reduction in the state space of an MDP and thus scale to problem sizes that are beyond the reach of classical MDP algorithms. However, factored MDPs are typically solved using custom-designed algorithms that can require meticulous implementations and considerable fine-tuning. In this paper, we propose a mathematical programming approach to solving factored MDPs. In contrast to existing solution schemes, our approach leverages off-the-shelf solvers, which allows for a streamlined implementation and maintenance; it effectively capitalizes on the factored structure present in both state and action spaces; and it readily extends to the largely unexplored class of robust factored MDPs, whose transition kernels are only known to reside in a pre-specified ambiguity set. Our numerical experiments demonstrate the potential of our approach.
Talk 3: A Deep Learning Approach to Multistage Stochastic Programming
Speaker: Rui Gao
Abstract: Multistage stochastic programming problems are challenging due to the curse of dimensionality. We introduce a practical algorithm for solving multistage stochastic programming in high dimensions, leveraging neural networks to parameterize the policy. The proposed algorithm demonstrates effectiveness in terms of both accuracy and speed across a variety of problems.
