ICML 2023 Papers

A neural network consisting of piecewise affine building blocks, such as fully-connected layers and ReLU activations, is itself a piecewise affine function supported on a polyhedral complex. This complex has been previously studied to characterize theoretical properties of neural networks, but, in practice, extracting it remains a challenge due to its high combinatorial complexity. A natural idea described in previous works is to subdivide the regions via intersections with hyperplanes induced by each neuron. However, we argue that this view leads to computational redundancy. Instead of regions, we propose to subdivide edges, leading to a novel method for polyhedral complex extraction. A key to this are sign-vectors, which encode the combinatorial structure of the complex. Our approach allows to use standard tensor operations on a GPU, taking seconds for millions of cells on a consumer grade machine. Motivated by the growing interest in neural shape representation, we use the speed and differentiablility of our method to optimize geometric properties of the complex. The code is available at https://github.com/arturs-berzins/relu_edge_subdivision.

Stochastic optimization is one of the central problems in Machine Learning and Theoretical Computer Science. In the standard model, the algorithm is given a fixed distribution known in advance. In practice though, one may acquire at a cost extra information to make better decisions. In this paper, we study how to buy information for stochastic optimization and formulate this question as an online learning problem. Assuming the learner has an oracle for the original optimization problem, we design a $2$-competitive deterministic algorithm and a $e/(e-1)$-competitive randomized algorithm for buying information. We show that this ratio is tight as the problem is equivalent to a robust generalization of the ski-rental problem, which we call super-martingale stopping. We also consider an adaptive setting where the learner can choose to buy information after taking some actions for the underlying optimization problem. We focus on the classic optimization problem, Min-Sum Set Cover, where the goal is to quickly find an action that covers a given request drawn from a known distribution. We provide an $8$-competitive algorithm running in polynomial time that chooses actions and decides when to buy information about the underlying request.

Leveraging privileged information (PI), or features available during training but not at test time, has recently been shown to be an effective method for addressing label noise. However, the reasons for its effectiveness are not well understood. In this study, we investigate the role played by different properties of the PI in explaining away label noise. Through experiments on multiple datasets with real PI (CIFAR-N/H) and a new large-scale benchmark ImageNet-PI, we find that PI is most helpful when it allows networks to easily distinguish clean from noisy data, while enabling a learning shortcut to memorize the noisy examples. Interestingly, when PI becomes too predictive of the target label, PI methods often perform worse than their no-PI baselines. Based on these findings, we propose several enhancements to the state-of-the-art PI methods and demonstrate the potential of PI as a means of tackling label noise. Finally, we show how we can easily combine the resulting PI approaches with existing no-PI techniques designed to deal with label noise.

In recent years, online search has been playing an increasingly important role in imperfect information games (IIGs). Previous online search is known as common-knowledge subgame solving, which has to consider all the states in a common-knowledge closure. This is only computationally tolerable for medium size games, such as poker. To handle larger games, order-1 Knowledge-Limited Subgame Solving (1-KLSS) only considers the states in a knowledge-limited closure, which results in a much smaller subgame. However, 1-KLSS is unsafe. In this paper, we first extend 1-KLSS to Safe-1-KLSS and prove its safeness. To make Safe-1-KLSS applicable to even larger games, we propose Opponent-Limited Subgame Solving (OLSS) to limit how the opponent reaches a subgame and how it acts in the subgame. Limiting the opponent's strategy dramatically reduces the subgame size and improves the efficiency of subgame solving while still preserving some safety in the limit. Experiments in medium size poker show that Safe-1-KLSS and OLSS are orders of magnitude faster than previous common-knowledge subgame solving. Also, OLSS significantly improves the online performance in a two-player Mahjong game, whose game size prohibits the use of previous common-knowledge subgame-solving methods.

We formalize the problem of contextual optimization through the lens of Bayesian experimental design and propose CO-BED---a general, model-agnostic framework for designing contextual experiments using information-theoretic principles. After formulating a suitable information-based objective, we employ black-box variational methods to simultaneously estimate it and optimize the designs in a single stochastic gradient scheme. In addition, to accommodate discrete actions within our framework, we propose leveraging continuous relaxation schemes, which can naturally be integrated into our variational objective. As a result, CO-BED provides a general and automated solution to a wide range of contextual optimization problems. We illustrate its effectiveness in a number of experiments, where CO-BED demonstrates competitive performance even when compared to bespoke, model-specific alternatives.