Arnaud Sors

Darko Drakulic, Sofia Michel, Florian Mai et al.

Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge. In this paper, we present a novel formulation of Combinatorial Optimization Problems (COPs) as Markov Decision Processes (MDPs) that effectively leverages common symmetries of COPs to improve out-of-distribution robustness. Starting from a direct MDP formulation of a constructive method, we introduce a generic way to reduce the state space, based on Bisimulation Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize the bisimulation and show how the reduced state exploits the symmetries of these problems and facilitates MDP solving. Our approach is principled and we prove that an optimal policy for the proposed BQ-MDP actually solves the associated COPs. We illustrate our approach on five classical problems: the Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing, Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce a simple attention-based policy network for the BQ-MDPs, which we train by imitation of (near) optimal solutions of small instances from a single distribution. We obtain new state-of-the-art results for the five COPs on both synthetic and realistic benchmarks. Notably, in contrast to most existing neural approaches, our learned policies show excellent generalization performance to much larger instances than seen during training, without any additional search procedure.

Arnaud Sors, Rafael Sampaio de Rezende, Sarah Ibrahimi et al.

Contrastive losses have long been a key ingredient of deep metric learning and are now becoming more popular due to the success of self-supervised learning. Recent research has shown the benefit of decomposing such losses into two sub-losses which act in a complementary way when learning the representation network: a positive term and an entropy term. Although the overall loss is thus defined as a combination of two terms, the balance of these two terms is often hidden behind implementation details and is largely ignored and sub-optimal in practice. In this work, we approach the balance of contrastive losses as a hyper-parameter optimization problem, and propose a coordinate descent-based search method that efficiently find the hyper-parameters that optimize evaluation performance. In the process, we extend existing balance analyses to the contrastive margin loss, include batch size in the balance, and explain how to aggregate loss elements from the batch to maintain near-optimal performance over a larger range of batch sizes. Extensive experiments with benchmarks from deep metric learning and self-supervised learning show that optimal hyper-parameters are found faster with our method than with other common search methods.

Sarah Ibrahimi, Arnaud Sors, Rafael Sampaio de Rezende et al.

Learning with noisy labels is an active research area for image classification. However, the effect of noisy labels on image retrieval has been less studied. In this work, we propose a noise-resistant method for image retrieval named Teacher-based Selection of Interactions, T-SINT, which identifies noisy interactions, ie. elements in the distance matrix, and selects correct positive and negative interactions to be considered in the retrieval loss by using a teacher-based training setup which contributes to the stability. As a result, it consistently outperforms state-of-the-art methods on high noise rates across benchmark datasets with synthetic noise and more realistic noise.