Patrick Thiran

Saeed Masiha, Sepehr Elahi, Negar Kiyavash et al.

We study Stackelberg (leader--follower) tuning of network parameters (tolls, capacities, incentives) in combinatorial congestion games, where selfish users choose discrete routes (or other combinatorial strategies) and settle at a congestion equilibrium. The leader minimizes a system-level objective (e.g., total travel time) evaluated at equilibrium, but this objective is typically nonsmooth because the set of used strategies can change abruptly. We propose ZO-Stackelberg, which couples a projection-free Frank--Wolfe equilibrium solver with a zeroth-order outer update, avoiding differentiation through equilibria. We prove convergence to generalized Goldstein stationary points of the true equilibrium objective, with explicit dependence on the equilibrium approximation error, and analyze subsampled oracles: if an exact minimizer is sampled with probability $κ_m$, then the Frank--Wolfe error decays as $\mathcal{O}(1/(κ_m T))$. We also propose stratified sampling as a practical way to avoid a vanishing $κ_m$ when the strategies that matter most for the Wardrop equilibrium concentrate in a few dominant combinatorial classes (e.g., short paths). Experiments on real-world networks demonstrate that our method achieves orders-of-magnitude speedups over a differentiation-based baseline while converging to follower equilibria.

Anthony Bardou, Patrick Thiran, Thomas Begin

Bayesian Optimization (BO) is typically used to optimize an unknown function $f$ that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Even if provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open problem, often tackled by assuming an additive structure for $f$. By doing so, BO algorithms typically introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. This paper contains two main contributions: (i) we relax the restrictive assumptions on the additive structure of $f$ without weakening the maximization guarantees of the acquisition function, and (ii) we address the over-exploration problem for decentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms, especially when the additive structure of $f$ comprises high-dimensional factors.