Session: Bilevel Optimization - Applications
Chair: Tommaso Giovannelli
Cluster: nan
Talk 1: (Canceled) Optimal Electric Vehicle Charging with Dynamic Pricing, Customer Preferences and Power Peak Reduction
Speaker: Luce Brotcorne
Abstract: (Canceled) We consider a provider of electric vehicle charging stations that operates a network of charging stations and use time varying pricing to maximize profit and reduce the impact on the electric grid. We propose a bilevel model with a single leader and multiple disjoint followers. The provider (leader) sets the price of charging for each station at each time slot, and ensures there is enough energy to charge. The charging choice of each customer is represented by a combination of a preference list of (station, time) pairs and a reserve price. The proposed model takes thus into accounts for the heterogeneity of customers with respect to price sensitivity. We define a single-level reformulation based on a reformulation approach from the literature on product line optimization, and we report computational results that highlight the efficiency of the new reformulation and the potential impact for reducing peaks on the electricity grid.
Talk 2: A Stochastic Gradient Method for Trilevel Optimization
Speaker: Tommaso Giovannelli
Abstract: With the recent success of bilevel optimization in machine learning applications, stochastic optimization formulations have begun to emerge for trilevel optimization, such as those involving hyperparameter tuning via adversarial training. In these formulations, the upper level minimizes the loss on validation data over the neural network's hyperparameters, the middle level determines the weights to minimize the loss on the training data, and the lower level maximizes such a training loss by adding worst-case perturbations to the data. The challenge is that trilevel first-order methods require second- or third-order derivatives, which become impractical to compute in problems involving a large number of variables. In this work, we propose the first-ever stochastic gradient descent method for solving unconstrained trilevel optimization problems. We also present a convergence theory that covers all inexact calculations of the trilevel adjoint gradient, such as the inexact solutions of the middle- and lower-level problems, inexact computation of the adjoint formula, and noisy estimates of the gradients, Hessians, Jacobians, and tensors of third-order derivatives involved. To promote the use of trilevel optimization in large-scale learning, we have developed practical trilevel stochastic gradient methods that extend approaches proposed for bilevel optimization and do not require second- or third-order derivatives.
Talk 3: Learning prosumer behavior in energy communities: Fusing bilevel programming and online learning
Speaker: Lesia Mitridati
Abstract: Dynamic pricing through bilevel programming is widely used for demand response but often assumes perfect knowledge of prosumer behavior, which is unrealistic in practical applications. This paper presents a novel framework that integrates bilevel programming with online learning, specifically Thompson sampling, to overcome this limitation. The approach dynamically sets optimal prices while simultaneously learning prosumer behaviors through observed responses, eliminating the need for extensive pre-existing datasets. Applied to an energy community providing capacity limitation services to a distribution system operator, the framework allows the community manager to infer individual prosumer characteristics, including usage patterns for photovoltaic systems, electric vehicles, home batteries, and heat pumps. Numerical simulations with 25 prosumers, each represented by 10 potential signatures, demonstrate rapid learning with low regret, with most prosumer characteristics learned within five days and full convergence achieved in 100 days.
