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Register a new userSemi-bandit Optimization in the Dispersed Setting
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The goal of data-driven algorithm design is to obtain high-performing algorithms for specific application domains using machine learning and data. Across many fields in AI, science, and engineering, practitioners will often fix a family of parameterized algorithms and then optimize those parameters to obtain good performance on example instances from the application domain. In the online setting, we must choose algorithm parameters for each instance as they arrive, and our goal is to be competitive with the best fixed algorithm in hindsight. There are two major challenges in online data-driven algorithm design. First, it can be computationally expensive to evaluate the loss functions that map algorithm parameters to performance, which often require the learner to run a combinatorial algorithm to measure its performance. Second, the losses can be extremely volatile and have sharp discontinuities. However, we show that in many applications, evaluating the loss function for one algorithm choice can sometimes reveal the loss for a range of similar algorithms, essentially for free. We develop online optimization algorithms capable of using this kind of extra information by working in the semi-bandit feedback setting. Our algorithms achieve regret bounds that are essentially as good as algorithms under full-information feedback and are significantly more computationally efficient. We apply our semi-bandit results to obtain the first provable guarantees for data-driven algorithm design for linkage-based clustering and we improve the best regret bounds for designing greedy knapsack algorithms.
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Bandit Convex Optimization (BCO) is a fundamental framework for modeling sequential decision-making with partial information, where the only feedback available to the player is the one-point or two-point function values. In this paper, we investigate BCO in non-stationary environments and choose the emph{dynamic regret} as the performance measure, which is defined as the difference between the cumulative loss incurred by the algorithm and that of any feasible comparator sequence. Let $T$ be the time horizon and $P_T$ be the path-length of the comparator sequence that reflects the non-stationarity of environments. We propose a novel algorithm that achieves $O(T^{3/4}(1+P_T)^{1/2})$ and $O(T^{1/2}(1+P_T)^{1/2})$ dynamic regret respectively for the one-point and two-point feedback models. The latter result is optimal, matching the $Omega(T^{1/2}(1+P_T)^{1/2})$ lower bound established in this paper. Notably, our algorithm is more adaptive to non-stationary environments since it does not require prior knowledge of the path-length $P_T$ ahead of time, which is generally unknown.
We formulate a new problem at the intersectionof semi-supervised learning and contextual bandits,motivated by several applications including clini-cal trials and ad recommendations. We demonstratehow Graph Convolutional Network (GCN), a semi-supervised learning approach, can be adjusted tothe new problem formulation. We also propose avariant of the linear contextual bandit with semi-supervised missing rewards imputation. We thentake the best of both approaches to develop multi-GCN embedded contextual bandit. Our algorithmsare verified on several real world datasets.
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.
Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While recent approaches use Bayesian optimization to adaptively select configurations, we focus on speeding up random search through adaptive resource allocation and early-stopping. We formulate hyperparameter optimization as a pure-exploration non-stochastic infinite-armed bandit problem where a predefined resource like iterations, data samples, or features is allocated to randomly sampled configurations. We introduce a novel algorithm, Hyperband, for this framework and analyze its theoretical properties, providing several desirable guarantees. Furthermore, we compare Hyperband with popular Bayesian optimization methods on a suite of hyperparameter optimization problems. We observe that Hyperband can provide over an order-of-magnitude speedup over our competitor set on a variety of deep-learning and kernel-based learning problems.
Bandit problems with linear or concave reward have been extensively studied, but relatively few works have studied bandits with non-concave reward. This work considers a large family of bandit problems where the unknown underlying reward function is non-concave, including the low-rank generalized linear bandit problems and two-layer neural network with polynomial activation bandit problem. For the low-rank generalized linear bandit problem, we provide a minimax-optimal algorithm in the dimension, refuting both conjectures in [LMT21, JWWN19]. Our algorithms are based on a unified zeroth-order optimization paradigm that applies in great generality and attains optimal rates in several structured polynomial settings (in the dimension). We further demonstrate the applicability of our algorithms in RL in the generative model setting, resulting in improved sample complexity over prior approaches. Finally, we show that the standard optimistic algorithms (e.g., UCB) are sub-optimal by dimension factors. In the neural net setting (with polynomial activation functions) with noiseless reward, we provide a bandit algorithm with sample complexity equal to the intrinsic algebraic dimension. Again, we show that optimistic approaches have worse sample complexity, polynomial in the extrinsic dimension (which could be exponentially worse in the polynomial degree).
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