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We consider the problem of controlling an unknown linear time-invariant dynamical system from a single chain of black-box interactions, with no access to resets or offline simulation. Under the assumption that the system is controllable, we give the first efficient algorithm that is capable of attaining sublinear regret in a single trajectory under the setting of online nonstochastic control. This resolves an open problem on the stochastic LQR problem, and in a more challenging setting that allows for adversarial perturbations and adversarially chosen and changing convex loss functions. We give finite-time regret bounds for our algorithm on the order of $2^{tilde{O}(mathcal{L})} + tilde{O}(text{poly}(mathcal{L}) T^{2/3})$ for general nonstochastic control, and $2^{tilde{O}(mathcal{L})} + tilde{O}(text{poly}(mathcal{L}) sqrt{T})$ for black-box LQR, where $mathcal{L}$ is the system size which is an upper bound on the dimension. The crucial step is a new system identification method that is robust to adversarial noise, but incurs exponential cost. To complete the picture, we investigate the complexity of the online black-box control problem, and give a matching lower bound of $2^{Omega(mathcal{L})}$ on the regret, showing that the additional exponential cost is inevitable. This lower bound holds even in the noiseless setting, and applies to any, randomized or deterministic, black-box control method.
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Most existing black-box optimization methods assume that all variables in the system being optimized have equal cost and can change freely at each iteration. However, in many real world systems, inputs are passed through a sequence of different operations or modules, making variables in earlier stages of processing more costly to update. Such structure imposes a cost on switching variables in early parts of a data processing pipeline. In this work, we propose a new algorithm for switch cost-aware optimization called Lazy Modular Bayesian Optimization (LaMBO). This method efficiently identifies the global optimum while minimizing cost through a passive change of variables in early modules. The method is theoretical grounded and achieves vanishing regret when augmented with switching cost. We apply LaMBO to multiple synthetic functions and a three-stage image segmentation pipeline used in a neuroscience application, where we obtain promising improvements over prevailing cost-aware Bayesian optimization algorithms. Our results demonstrate that LaMBO is an effective strategy for black-box optimization that is capable of minimizing switching costs in modular systems.
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We derive an optimal policy for adaptively restarting a randomized algorithm, based on observed features of the run-so-far, so as to minimize the expected time required for the algorithm to successfully terminate. Given a suitable Bayesian prior, this result can be used to select the optimal black-box optimization algorithm from among a large family of algorithms that includes random search, Successive Halving, and Hyperband. On CIFAR-10 and ImageNet hyperparameter tuning problems, the proposed policies offer up to a factor of 13 improvement over random search in terms of expected time to reach a given target accuracy, and up to a factor of 3 improvement over a baseline adaptive policy that terminates a run whenever its accuracy is below-median.
Transfer learning has become a common practice for training deep learning models with limited labeled data in a target domain. On the other hand, deep models are vulnerable to adversarial attacks. Though transfer learning has been widely applied, its effect on model robustness is unclear. To figure out this problem, we conduct extensive empirical evaluations to show that fine-tuning effectively enhances model robustness under white-box FGSM attacks. We also propose a black-box attack method for transfer learning models which attacks the target model with the adversarial examples produced by its source model. To systematically measure the effect of both white-box and black-box attacks, we propose a new metric to evaluate how transferable are the adversarial examples produced by a source model to a target model. Empirical results show that the adversarial examples are more transferable when fine-tuning is used than they are when the two networks are trained independently.
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