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We investigate the use of a non-parametric independence measure, the Hilbert-Schmidt Independence Criterion (HSIC), as a loss-function for learning robust regression and classification models. This loss-function encourages learning models where the distribution of the residuals between the label and the model prediction is statistically independent of the distribution of the instances themselves. This loss-function was first proposed by Mooij et al. (2009) in the context of learning causal graphs. We adapt it to the task of learning for unsupervised covariate shift: learning on a source domain without access to any instances or labels from the unknown target domain, but with the assumption that $p(y|x)$ (the conditional probability of labels given instances) remains the same in the target domain. We show that the proposed loss is expected to give rise to models that generalize well on a class of target domains characterised by the complexity of their description within a reproducing kernel Hilbert space. Experiments on unsupervised covariate shift tasks demonstrate that models learned with the proposed loss-function outperform models learned with standard loss functions, achieving state-of-the-art results on a challenging cell-microscopy unsupervised covariate shift task.
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The Hilbert Schmidt Independence Criterion (HSIC) is a kernel dependence measure that has applications in various aspects of machine learning. Conveniently, the objectives of different dimensionality reduction applications using HSIC often reduce to the same optimization problem. However, the nonconvexity of the objective function arising from non-linear kernels poses a serious challenge to optimization efficiency and limits the potential of HSIC-based formulations. As a result, only linear kernels have been computationally tractable in practice. This paper proposes a spectral-based optimization algorithm that extends beyond the linear kernel. The algorithm identifies a family of suitable kernels and provides the first and second-order local guarantees when a fixed point is reached. Furthermore, we propose a principled initialization strategy, thereby removing the need to repeat the algorithm at random initialization points. Compared to state-of-the-art optimization algorithms, our empirical results on real data show a run-time improvement by as much as a factor of $10^5$ while consistently achieving lower cost and classification/clustering errors. The implementation source code is publicly available on https://github.com/endsley.
Robust Reinforcement Learning aims to find the optimal policy with some extent of robustness to environmental dynamics. Existing learning algorithms usually enable the robustness through disturbing the current state or simulating environmental parameters in a heuristic way, which lack quantified robustness to the system dynamics (i.e. transition probability). To overcome this issue, we leverage Wasserstein distance to measure the disturbance to the reference transition kernel. With Wasserstein distance, we are able to connect transition kernel disturbance to the state disturbance, i.e. reduce an infinite-dimensional optimization problem to a finite-dimensional risk-aware problem. Through the derived risk-aware optimal Bellman equation, we show the existence of optimal robust policies, provide a sensitivity analysis for the perturbations, and then design a novel robust learning algorithm--Wasserstein Robust Advantage Actor-Critic algorithm (WRAAC). The effectiveness of the proposed algorithm is verified in the Cart-Pole environment.
Robust loss minimization is an important strategy for handling robust learning issue on noisy labels. Current robust loss functions, however, inevitably involve hyperparameter(s) to be tuned, manually or heuristically through cross validation, which makes them fairly hard to be generally applied in practice. Besides, the non-convexity brought by the loss as well as the complicated network architecture makes it easily trapped into an unexpected solution with poor generalization capability. To address above issues, we propose a meta-learning method capable of adaptively learning hyperparameter in robust loss functions. Specifically, through mutual amelioration between robust loss hyperparameter and network parameters in our method, both of them can be simultaneously finely learned and coordinated to attain solutions with good generalization capability. Four kinds of SOTA robust loss functions are attempted to be integrated into our algorithm, and comprehensive experiments substantiate the general availability and effectiveness of the proposed method in both its accuracy and generalization performance, as compared with conventional hyperparameter tuning strategy, even with carefully tuned hyperparameters.
We propose a new approach to train a variational information bottleneck (VIB) that improves its robustness to adversarial perturbations. Unlike the traditional methods where the hard labels are usually used for the classification task, we refine the categorical class information in the training phase with soft labels which are obtained from a pre-trained reference neural network and can reflect the likelihood of the original class labels. We also relax the Gaussian posterior assumption in the VIB implementation by using the mutual information neural estimation. Extensive experiments have been performed with the MNIST and CIFAR-10 datasets, and the results show that our proposed approach significantly outperforms the benchmarked models.
We introduce a sampling perspective to tackle the challenging task of training robust Reinforcement Learning (RL) agents. Leveraging the powerful Stochastic Gradient Langevin Dynamics, we present a novel, scalable two-player RL algorithm, which is a sampling variant of the two-player policy gradient method. Our algorithm consistently outperforms existing baselines, in terms of generalization across different training and testing conditions, on several MuJoCo environments. Our experiments also show that, even for objective functions that entirely ignore potential environmental shifts, our sampling approach remains highly robust in comparison to standard RL algorithms.
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