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Register a new userEfficient Batch Black-box Optimization with Deterministic Regret Bounds
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In this work, we investigate black-box optimization from the perspective of frequentist kernel methods. We propose a novel batch optimization algorithm, which jointly maximizes the acquisition function and select points from a whole batch in a holistic way. Theoretically, we derive regret bounds for both the noise-free and perturbation settings irrespective of the choice of kernel. Moreover, we analyze the property of the adversarial regret that is required by a robust initialization for Bayesian Optimization (BO). We prove that the adversarial regret bounds decrease with the decrease of covering radius, which provides a criterion for generating a point set to minimize the bound. We then propose fast searching algorithms to generate a point set with a small covering radius for the robust initialization. Experimental results on both synthetic benchmark problems and real-world problems show the effectiveness of the proposed algorithms.
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This paper analyses the problem of Gaussian process (GP) bandits with deterministic observations. The analysis uses a branch and bound algorithm that is related to the UCB algorithm of (Srinivas et al., 2010). For GPs with Gaussian observation noise, with variance strictly greater than zero, (Srinivas et al., 2010) proved that the regret vanishes at the approximate rate of $O(frac{1}{sqrt{t}})$, where t is the number of observations. To complement their result, we attack the deterministic case and attain a much faster exponential convergence rate. Under some regularity assumptions, we show that the regret decreases asymptotically according to $O(e^{-frac{tau t}{(ln t)^{d/4}}})$ with high probability. Here, d is the dimension of the search space and $tau$ is a constant that depends on the behaviour of the objective function near its global maximum.
This paper analyzes the problem of Gaussian process (GP) bandits with deterministic observations. The analysis uses a branch and bound algorithm that is related to the UCB algorithm of (Srinivas et al, 2010). For GPs with Gaussian observation noise, with variance strictly greater than zero, Srinivas et al proved that the regret vanishes at the approximate rate of $O(1/sqrt{t})$, where t is the number of observations. To complement their result, we attack the deterministic case and attain a much faster exponential convergence rate. Under some regularity assumptions, we show that the regret decreases asymptotically according to $O(e^{-frac{tau t}{(ln t)^{d/4}}})$ with high probability. Here, d is the dimension of the search space and tau is a constant that depends on the behaviour of the objective function near its global maximum.
Many applications require a learner to make sequential decisions given uncertainty regarding both the systems payoff function and safety constraints. In safety-critical systems, it is paramount that the learners actions do not violate the safety constraints at any stage of the learning process. In this paper, we study a stochastic bandit optimization problem where the unknown payoff and constraint functions are sampled from Gaussian Processes (GPs) first considered in [Srinivas et al., 2010]. We develop a safe variant of GP-UCB called SGP-UCB, with necessary modifications to respect safety constraints at every round. The algorithm has two distinct phases. The first phase seeks to estimate the set of safe actions in the decision set, while the second phase follows the GP-UCB decision rule. Our main contribution is to derive the first sub-linear regret bounds for this problem. We numerically compare SGP-UCB against existing safe Bayesian GP optimization algorithms.
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.
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.
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