Abstracting Imperfect Information Away from Two-Player Zero-Sum Games

In their seminal work, Nayyar et al. (2013) showed that imperfect information can be abstracted away from common-payoff games by having players publicly announce their policies as they play. This insight underpins sound solvers and decision-time planning algorithms for common-payoff games. Unfortunately, a naive application of the same insight to two-player zero-sum games fails because Nash equilibria of the game with public policy announcements may not correspond to Nash equilibria of the original game. As a consequence, existing sound decision-time planning algorithms require complicated additional mechanisms that have unappealing properties. The main contribution of this work is showing that certain regularized equilibria do not possess the aforementioned non-correspondence problem -- thus, computing them can be treated as perfect information problems. Because these regularized equilibria can be made arbitrarily close to Nash equilibria, our result opens the door to a new perspective on solving two-player zero-sum games and, in particular, yields a simplified framework for decision-time planning in two-player zero-sum games, void of the unappealing properties that plague existing decision-time planning approaches.

Function Approximation for Solving Stackelberg Equilibrium in Large Perfect Information Games

Function approximation (FA) has been a critical component in solving large zero-sum games. Yet, little attention has been given towards FA in solving \textit{general-sum} extensive-form games, despite them being widely regarded as being computationally more challenging than their fully competitive or cooperative counterparts. A key challenge is that for many equilibria in general-sum games, no simple analogue to the state value function used in Markov Decision Processes and zero-sum games exists. In this paper, we propose learning the \textit{Enforceable Payoff Frontier} (EPF) -- a generalization of the state value function for general-sum games. We approximate the optimal \textit{Stackelberg extensive-form correlated equilibrium} by representing EPFs with neural networks and training them by using appropriate backup operations and loss functions. This is the first method that applies FA to the Stackelberg setting, allowing us to scale to much larger games while still enjoying performance guarantees based on FA error. Additionally, our proposed method guarantees incentive compatibility and is easy to evaluate without having to depend on self-play or approximate best-response oracles.

Losses over Labels: Weakly Supervised Learning via Direct Loss Construction

Owing to the prohibitive costs of generating large amounts of labeled data, programmatic weak supervision is a growing paradigm within machine learning. In this setting, users design heuristics that provide noisy labels for subsets of the data. These weak labels are combined (typically via a graphical model) to form pseudolabels, which are then used to train a downstream model. In this work, we question a foundational premise of the typical weakly supervised learning pipeline: given that the heuristic provides all ``label" information, why do we need to generate pseudolabels at all? Instead, we propose to directly transform the heuristics themselves into corresponding loss functions that penalize differences between our model and the heuristic. By constructing losses directly from the heuristics, we can incorporate more information than is used in the standard weakly supervised pipeline, such as how the heuristics make their decisions, which explicitly informs feature selection during training. We call our method Losses over Labels (LoL) as it creates losses directly from heuristics without going through the intermediate step of a label. We show that LoL improves upon existing weak supervision methods on several benchmark text and image classification tasks and further demonstrate that incorporating gradient information leads to better performance on almost every task.

Simple initialization and parametrization of sinusoidal networks via their kernel bandwidth

Neural networks with sinusoidal activations have been proposed as an alternative to networks with traditional activation functions. Despite their promise, particularly for learning implicit models, their training behavior is not yet fully understood, leading to a number of empirical design choices that are not well justified. In this work, we first propose a simplified version of such sinusoidal neural networks, which allows both for easier practical implementation and simpler theoretical analysis. We then analyze the behavior of these networks from the neural tangent kernel perspective and demonstrate that their kernel approximates a low-pass filter with an adjustable bandwidth. Finally, we utilize these insights to inform the sinusoidal network initialization, optimizing their performance for each of a series of tasks, including learning implicit models and solving differential equations.

Characterizing Datapoints via Second-Split Forgetting

Researchers investigating example hardness have increasingly focused on the dynamics by which neural networks learn and forget examples throughout training. Popular metrics derived from these dynamics include (i) the epoch at which examples are first correctly classified; (ii) the number of times their predictions flip during training; and (iii) whether their prediction flips if they are held out. However, these metrics do not distinguish among examples that are hard for distinct reasons, such as membership in a rare subpopulation, being mislabeled, or belonging to a complex subpopulation. In this paper, we propose $second$-$split$ $forgetting$ $time$ (SSFT), a complementary metric that tracks the epoch (if any) after which an original training example is forgotten as the network is fine-tuned on a randomly held out partition of the data. Across multiple benchmark datasets and modalities, we demonstrate that $mislabeled$ examples are forgotten quickly, and seemingly $rare$ examples are forgotten comparatively slowly. By contrast, metrics only considering the first split learning dynamics struggle to differentiate the two. At large learning rates, SSFT tends to be robust across architectures, optimizers, and random seeds. From a practical standpoint, the SSFT can (i) help to identify mislabeled samples, the removal of which improves generalization; and (ii) provide insights about failure modes. Through theoretical analysis addressing overparameterized linear models, we provide insights into how the observed phenomena may arise. Code for reproducing our experiments can be found here: https://github.com/pratyushmaini/ssft

Perfectly Secure Steganography Using Minimum Entropy Coupling

Steganography is the practice of encoding secret information into innocuous content in such a manner that an adversarial third party would not realize that there is hidden meaning. While this problem has classically been studied in security literature, recent advances in generative models have led to a shared interest among security and machine learning researchers in developing scalable steganography techniques. In this work, we show that a steganography procedure is perfectly secure under \citet{cachin_perfect}'s information theoretic-model of steganography if and only if it is induced by a coupling. Furthermore, we show that, among perfectly secure procedures, a procedure is maximally efficient if and only if it is induced by a minimum entropy coupling. These insights yield what are, to the best of our knowledge, the first steganography algorithms to achieve perfect security guarantees with non-trivial efficiency; additionally, these algorithms are highly scalable. To provide empirical validation, we compare a minimum entropy coupling-based approach to three modern baselines -- arithmetic coding, Meteor, and adaptive dynamic grouping -- using GPT-2 and WaveRNN as communication channels. We find that the minimum entropy coupling-based approach yields superior encoding efficiency, despite its stronger security constraints. In aggregate, these results suggest that it may be natural to view information-theoretic steganography through the lens of minimum entropy coupling.

Understanding the Covariance Structure of Convolutional Filters

Neural network weights are typically initialized at random from univariate distributions, controlling just the variance of individual weights even in highly-structured operations like convolutions. Recent ViT-inspired convolutional networks such as ConvMixer and ConvNeXt use large-kernel depthwise convolutions whose learned filters have notable structure; this presents an opportunity to study their empirical covariances. In this work, we first observe that such learned filters have highly-structured covariance matrices, and moreover, we find that covariances calculated from small networks may be used to effectively initialize a variety of larger networks of different depths, widths, patch sizes, and kernel sizes, indicating a degree of model-independence to the covariance structure. Motivated by these findings, we then propose a learning-free multivariate initialization scheme for convolutional filters using a simple, closed-form construction of their covariance. Models using our initialization outperform those using traditional univariate initializations, and typically meet or exceed the performance of those initialized from the covariances of learned filters; in some cases, this improvement can be achieved without training the depthwise convolutional filters at all.

General Cutting Planes for Bound-Propagation-Based Neural Network Verification

Bound propagation methods, when combined with branch and bound, are among the most effective methods to formally verify properties of deep neural networks such as correctness, robustness, and safety. However, existing works cannot handle the general form of cutting plane constraints widely accepted in traditional solvers, which are crucial for strengthening verifiers with tightened convex relaxations. In this paper, we generalize the bound propagation procedure to allow the addition of arbitrary cutting plane constraints, including those involving relaxed integer variables that do not appear in existing bound propagation formulations. Our generalized bound propagation method, GCP-CROWN, opens up the opportunity to apply general cutting plane methods} for neural network verification while benefiting from the efficiency and GPU acceleration of bound propagation methods. As a case study, we investigate the use of cutting planes generated by off-the-shelf mixed integer programming (MIP) solver. We find that MIP solvers can generate high-quality cutting planes for strengthening bound-propagation-based verifiers using our new formulation. Since the branching-focused bound propagation procedure and the cutting-plane-focused MIP solver can run in parallel utilizing different types of hardware (GPUs and CPUs), their combination can quickly explore a large number of branches with strong cutting planes, leading to strong verification performance. Experiments demonstrate that our method is the first verifier that can completely solve the oval20 benchmark and verify twice as many instances on the oval21 benchmark compared to the best tool in VNN-COMP 2021, and also noticeably outperforms state-of-the-art verifiers on a wide range of benchmarks. GCP-CROWN is part of the $\alpha$,$\beta$-CROWN verifier, the VNN-COMP 2022 winner. Code is available at http://PaperCode.cc/GCP-CROWN

(Certified!!) Adversarial Robustness for Free!

In this paper we show how to achieve state-of-the-art certified adversarial robustness to 2-norm bounded perturbations by relying exclusively on off-the-shelf pretrained models. To do so, we instantiate the denoised smoothing approach of Salman et al. by combining a pretrained denoising diffusion probabilistic model and a standard high-accuracy classifier. This allows us to certify 71% accuracy on ImageNet under adversarial perturbations constrained to be within a 2-norm of 0.5, an improvement of 14 percentage points over the prior certified SoTA using any approach, or an improvement of 30 percentage points over denoised smoothing. We obtain these results using only pretrained diffusion models and image classifiers, without requiring any fine tuning or retraining of model parameters.

A Unified Approach to Reinforcement Learning, Quantal Response Equilibria, and Two-Player Zero-Sum Games

Algorithms designed for single-agent reinforcement learning (RL) generally fail to converge to equilibria in two-player zero-sum (2p0s) games. Conversely, game-theoretic algorithms for approximating Nash and quantal response equilibria (QREs) in 2p0s games are not typically competitive for RL and can be difficult to scale. As a result, algorithms for these two cases are generally developed and evaluated separately. In this work, we show that a single algorithm -- a simple extension to mirror descent with proximal regularization that we call magnetic mirror descent (MMD) -- can produce strong results in both settings, despite their fundamental differences. From a theoretical standpoint, we prove that MMD converges linearly to QREs in extensive-form games -- this is the first time linear convergence has been proven for a first order solver. Moreover, applied as a tabular Nash equilibrium solver via self-play, we show empirically that MMD produces results competitive with CFR in both normal-form and extensive-form games with full feedback (this is the first time that a standard RL algorithm has done so) and also that MMD empirically converges in black-box feedback settings. Furthermore, for single-agent deep RL, on a small collection of Atari and Mujoco games, we show that MMD can produce results competitive with those of PPO. Lastly, for multi-agent deep RL, we show MMD can outperform NFSP in 3x3 Abrupt Dark Hex.