Shijie Pan

Shijie Pan, Jianyu Xu, Wenjie Huang

A novel Follow-the-Perturbed-Leader type algorithm is proposed and analyzed for solving general long-term constrained optimization problems in an online manner, where the target and constraint functions are oblivious adversarially generated and not necessarily convex. The algorithm is based on Lagrangian reformulation and innovatively integrates random perturbations and regularizations in primal and dual directions: 1). exponentially distributed random perturbations in the primal direction to handle non-convexity, and 2). strongly concave logarithmic regularizations in the dual space to handle constraint violations. Based on a proposed expected static cumulative regret, and under mild Lipschitz continuity assumption, the algorithm demonstrates the online learnability, achieving the first sublinear cumulative regret complexity for this class of problems. The proposed algorithm is applied to tackle a long-term (extreme value) constrained river pollutant source identification problem, validate the theoretical results and exhibit superior performance compared to existing methods.

Shijie Pan, Zaint A. Alexakis, Charalambos Konstantinou

Data centers (DCs) are emerging as large, geographically distributed, controllable loads whose participation in electricity markets can significantly affect grid operation, especially when cloud platforms shift workloads across sites to exploit energy-arbitrage opportunities. This paper analyzes and seeks to mitigate the grid impacts of geographically distributed multi-site DCs under exogenous electricity prices. It develops a detailed job-level scheduling framework for market-driven DCs, formulated as a mixed-integer model that preserves execution logic and captures a unified set of implementable control actions. It also incorporates service-side quality-of-service (QoS) constraints and penalty terms to improve fidelity. Case studies on a modified IEEE 14-bus system, complemented by a more realistic network based on Travis County, Texas, show that purely price-driven scheduling improves economic performance, but also increases voltage-security risk and congestion exposure by inducing localized demand concentration and sharp site-level load variation. To mitigate these effects, this work introduces load-redistribution policies that curb extreme load shifting and support grid operators in managing such conditions.

Agustin Castellano, Shijie Pan, Enrique Mallada

Model Predictive Control (MPC) is a powerful framework for optimal control but can be too slow for low-latency applications. We present a data-driven framework to accelerate MPC by replacing online optimization with a nonparametric policy constructed from offline MPC solutions. Our policy is greedy with respect to a constructed upper bound on the optimal cost-to-go, and can be implemented as a nonparametric lookup rule that is orders of magnitude faster than solving MPC online. Our analysis shows that under sufficient coverage condition of the offline data, the policy is recursively feasible and admits provable, bounded optimality gap. These conditions establish an explicit trade-off between the amount of data collected and the tightness of the bounds. Our experiments show that this policy is between 100 and 1000 times faster than standard MPC, with only a modest hit to optimality, showing potential for real-time control tasks.