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1. Learning to Optimize Differentiable Games

   Chen, Xuxi; Vadori, Nelson; Chen, Tianlong; Wang, Zhangyang (July 2023, International Conference on Machine Learning)

   Many machine learning problems can be abstracted in solving game theory formulations and boil down to optimizing nested objectives, such as generative adversarial networks (GANs) and multi-agent reinforcement learning. Solving these games requires finding their stable fixed points or Nash equilibrium. However, existing algorithms for solving games suffer from empirical instability, hence demanding heavy ad-hoc tuning in practice. To tackle these challenges, we resort to the emerging scheme of Learning to Optimize (L2O), which discovers problem-specific efficient optimization algorithms through data-driven training. Our customized L2O framework for differentiable game theory problems, dubbed “Learning to Play Games" (L2PG), seeks a stable fixed point solution, by predicting the fast update direction from the past trajectory, with a novel gradient stability-aware, sign-based loss function. We further incorporate curriculum learning and self-learning to strengthen the empirical training stability and generalization of L2PG. On test problems including quadratic games and GANs, L2PG can substantially accelerate the convergence, and demonstrates a remarkably more stable trajectory. Codes are available at https://github.com/VITA-Group/L2PG. 

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2. Improved Robustness to Open Set Inputs via Tempered Mixup

   Roady, R.; Hayes, T.; Kanan, C. (January 2020, ECCV Workshop on Adversarial Robustness in the Real World (AROW))

   null (Ed.)

   Supervised classification methods often assume that evaluation data is drawn from the same distribution as training data and that all classes are present for training. However, real-world classifiers must handle inputs that are far from the training distribution including samples from unknown classes. Open set robustness refers to the ability to properly label samples from previously unseen categories as novel and avoid high-confidence, incorrect predictions. Existing approaches have focused on either novel inference methods, unique training architectures, or supplementing the training data with additional background samples. Here, we propose a simple regularization technique easily applied to existing convolutional neural network architectures that improves open set robustness without a background dataset. Our method achieves state-of-the-art results on open set classification baselines and easily scales to large-scale open set classification problems. 

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3. Learning to Generalize Provably in Learning to Optimize

   Yang, Junjie; Chen, Tianlong; Zhu, Mingkang; He, Fengxiang; Tao, Dacheng; Liang, Yingbin; Wang, Zhangyang (April 2023, International Conference on Artificial Intelligence and Statistics)

   Learning to optimize (L2O) has gained increasing popularity, which automates the design of optimizers by data-driven approaches. However, current L2O methods often suffer from poor generalization performance in at least two folds: (i) applying the L2O-learned optimizer to unseen optimizees, in terms of lowering their loss function values (optimizer generalization, or “generalizable learning of optimizers”); and (ii) the test performance of an optimizee (itself as a machine learning model), trained by the optimizer, in terms of the accuracy over unseen data (optimizee generalization, or “learning to generalize”). While the optimizer generalization has been recently studied, the optimizee generalization (or learning to generalize) has not been rigorously studied in the L2O context, which is the aim of this paper. We first theoretically establish an implicit connection between the local entropy and the Hessian, and hence unify their roles in the handcrafted design of generalizable optimizers as equivalent metrics of the landscape flatness of loss functions. We then propose to incorporate these two metrics as flatness-aware regularizers into the L2O framework in order to meta-train optimizers to learn to generalize, and theoretically show that such generalization ability can be learned during the L2O meta-training process and then transformed to the optimizee loss function. Extensive experiments consistently validate the effectiveness of our proposals with substantially improved generalization on multiple sophisticated L2O models and diverse optimizees. 

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4. Bilevel Coreset Selection in Continual Learning: A New Formulation and Algorithm

   Hao, J; Ji, K; Liu, M (February 2024, Advances in Neural Information Processing Systems)

   Coreset is a small set that provides a data summary for a large dataset, such that training solely on the small set achieves competitive performance compared with a large dataset. In rehearsal-based continual learning, the coreset is typically used in the memory replay buffer to stand for representative samples in previous tasks, and the coreset selection procedure is typically formulated as a bilevel problem. However, the typical bilevel formulation for coreset selection explicitly performs optimization over discrete decision variables with greedy search, which is computationally expensive. Several works consider other formulations to address this issue, but they ignore the nested nature of bilevel optimization problems and may not solve the bilevel coreset selection problem accurately. To address these issues, we propose a new bilevel formulation, where the inner problem tries to find a model which minimizes the expected training error sampled from a given probability distribution, and the outer problem aims to learn the probability distribution with approximately $$K$$ (coreset size) nonzero entries such that learned model in the inner problem minimizes the training error over the whole data. To ensure the learned probability has approximately $$K$$ nonzero entries, we introduce a novel regularizer based on the smoothed top-$$K$$ loss in the upper problem. We design a new optimization algorithm that provably converges to the $$\epsilon$$-stationary point with $$O(1/\epsilon^4)$$ computational complexity. We conduct extensive experiments in various settings in continual learning, including balanced data, imbalanced data, and label noise, to show that our proposed formulation and new algorithm significantly outperform competitive baselines. From bilevel optimization point of view, our algorithm significantly improves the vanilla greedy coreset selection method in terms of running time on continual learning benchmark datasets. The code is available at \url{https://github.com/MingruiLiu-ML-Lab/Bilevel-Coreset-Selection-via-Regularization}. 

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5. Bayesian Modeling and Uncertainty Quantification for Learning to Optimize: What, Why, and How

   You, Yuning; Cao, Yue; Chen, Tianlong; Wang, Zhangyang; Shen, Yang (April 2022, International Conference on Learning Representations)

   Optimizing an objective function with uncertainty awareness is well-known to improve the accuracy and confidence of optimization solutions. Meanwhile, another relevant but very different question remains yet open: how to model and quantify the uncertainty of an optimization algorithm (aka, optimizer) itself? To close such a gap, the prerequisite is to consider the optimizers as sampled from a distribution, rather than a few prefabricated and fixed update rules. We first take the novel angle to consider the algorithmic space of optimizers, and provide definitions for the optimizer prior and likelihood, that intrinsically determine the posterior and therefore uncertainty. We then leverage the recent advance of learning to optimize (L2O) for the space parameterization, with the end-to-end training pipeline built via variational inference, referred to as uncertainty-aware L2O (UA-L2O). Our study represents the first effort to recognize and quantify the uncertainty of the optimization algorithm. The extensive numerical results show that, UA-L2O achieves superior uncertainty calibration with accurate confidence estimation and tight confidence intervals, suggesting the improved posterior estimation thanks to considering optimizer uncertainty. Intriguingly, UA-L2O even improves optimization performances for two out of three test functions, the loss function in data privacy attack, and four of five cases of the energy function in protein docking. Our codes are released at https://github. com/Shen-Lab/Bayesian-L2O. 

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