Research Focus

Theory / Methodology

Optimization under Uncertainty

This research develops robust frameworks for decision-making under uncertainty, moving beyond simplistic assumptions to tackle real-world complexity.

Deterministic Optimization (DO) assumes all parameters are fixed and known perfectly ("The Optimistic View"). While computationally efficient, it is brittle; even small deviations from the forecast can render a solution infeasible. Stochastic Optimization (SO) incorporates randomness by assuming a known probability distribution for uncertain parameters ("The Risk-Neutral View"), minimizing expected costs. However, in reality, the true distribution is rarely known precisely. Distributionally Robust Optimization (DRO) addresses this "ambiguity" by defining a set of plausible distributions (an ambiguity set) consistent with available data. It then optimizes for the worst-case scenario within this set ("The Robust View"), ensuring reliability even when the underlying data model is imperfect.

Deterministic(DO)

$ \displaystyle \begin{aligned} \min \quad & c^\top x \\ \text{s.t.} \quad & Ax=b \end{aligned} $

+ Parameter Uncertainty

Stochastic(SO)

$ \displaystyle \min_{x \in X} \mathbb{E}[f(x, \xi)] $

+ Distribution Ambiguity

Robust(DRO)

$ \displaystyle \min_{x \in X} \max_{\mathbb{P} \in \mathcal{P}} \mathbb{E}_{\mathbb{P}}[f(x, \xi)] $

💡 Example: Inventory Management

Imagine you are ordering stock for a store.

DODeterministic: Assume demand is fixed (e.g., 100). Order 100.
SOStochastic: Demand fluctuates (e.g., weather-dependent). Order to maximize average profit.
DRODRO: The fluctuation pattern itself is unknown. Order to be safe against the worst-case scenario.

ML + Optimization Under Uncertainty

Integrated Machine Learning and Optimization under Uncertainty (Contextual Stochastic Optimization) Contextual stochastic optimization learns a decision rule $ z(X) $ that directly minimizes expected downstream cost under uncertainty. Instead of optimizing prediction accuracy first and decisions later ('Predict-then-Optimize'), it trains the predictive model and optimization layer jointly so that learned features are decision-relevant.

$ \displaystyle \min_{z \in \mathcal{Z}} \mathbb{E}[c(z, Y) \mid X = x] $

💡 Example: Energy Grid Optimization Instead of just minimizing forecast error for electricity demand, the model integrates with the scheduling optimization. It learns to penalize prediction errors that would cause expensive power shortages more heavily than over-supply, ensuring grid stability.
Distributionally Robust Learning Distributionally robust learning integrates Distributionally Robust Optimization (DRO) into model training. Instead of minimizing empirical risk under a single estimated distribution, it optimizes against an ambiguity set of plausible distributions, improving reliability under shift, noise, and subgroup imbalance.

$ \displaystyle \min_{\theta} \max_{g \in \mathcal{G}} \mathbb{E}_{(x,y) \sim P_g} [ \ell(f_\theta(x), y) ] $

💡 Example: Per-Group DRO Per-Group DRO is a specific example of distributionally robust learning designed to ensure both fairness and robustness. It addresses the limitation where standard models perform well on average but fail on specific sub-groups. By defining unique ambiguity sets for each demographic group and learning their sizes, the model is trained to protect worst-group performance while maintaining strong average performance.

Applications

We conduct applied research across diverse domains that require decision-making. Representative examples are listed below.

Resource Allocation

Natural Resources & Energy Systems

Subtopics: Water allocation, reservoir operation, energy scheduling.

Marketing Mix Modeling (MMM)

Subtopics: Channel response estimation, budget allocation, carryover effects.

Bidding Optimization

Subtopics: Auction modeling, bid policy learning, budget pacing.

Optimal Operations

Optimal Process Control

Subtopics: Process setpoint tuning, quality control, throughput improvement.

Hyperparameter Optimization

Subtopics: Bilevel optimization, Bayesian optimization, automated tuning.

Routing Optimization Under Uncertainty

Subtopics: Stochastic routing, delivery planning, robot navigation.