We introduce Meta-Album, an image classification meta-dataset designed to facilitate few-shot learning, transfer learning, meta-learning, among other tasks. It includes 40 open datasets, each having at least 20 classes with 40 examples per class, with verified licences. They stem from diverse domains, such as ecology (fauna and flora), manufacturing (textures, vehicles), human actions, and optical character recognition, featuring various image scales (microscopic, human scales, remote sensing). All datasets are preprocessed, annotated, and formatted uniformly, and come in 3 versions (Micro Mini Extended) to match users' computational resources.

Bayesian Optimization specifically aims to increase sample efficiency for hard optimization algorithms, and consequently can help achieve better solutions without incurring large societal costs. For instance, as demonstrated in this work, automotive design problems may be solved much faster, reducing the amount of computationally costly simulations and thus the energy footprint during development. At the same time, improved solutions mean that high crash safety can be achieved with lighter cars, resulting in fewer resources required for their production and, importantly, improving fuel economy of the whole vehicle fleet. Increased robustness to noisy observations further helps reduce the resources spent on evaluating regions of the search space that are not promising. Improvements to the optimization performance and practicality of multi-objective Bayesian optimization have the potential to allow decision makers to better understand and make more informed decisions across multiple trade-offs. We expect these directions to be particularly important as Bayesian optimization is increasingly used for applications such as recommender systems [35], where auxiliary goals such as fairness must be accounted for. Of course, at the end of the day, exactly what objectives decision makers choose to optimize, and how they balance those trade-offs (and whether that is done in equitable fashion) is up to the individuals themselves. Such a partitioning allows for efficient piece-wise computation of the hypervolume improvement from a new point f(xi) by computing the volume of the intersection of the region dominated exclusively by the new point with ({f(xi),P,r) (and not dominated by the P) with each hyperrectangle Sk.

Optimizing multiple competing black-box objectives is a challenging problem in many fields, including science, engineering, and machine learning. Multi-objective Bayesian optimization (MOBO) is a sample-efficient approach for identifying the optimal trade-offs between the objectives. However, many existing methods perform poorly when the observations are corrupted by noise. We propose a novel acquisition function, NEHVI, that overcomes this important practical limitation by applying a Bayesian treatment to the popular expected hypervolume improvement (EHVI) criterion and integrating over this uncertainty in the Pareto frontier. We argue that, even in the noiseless setting, generating multiple candidates in parallel is an incarnation of EHVI with uncertainty in the Pareto frontier and therefore can be addressed using the same underlying technique. Through this lens, we derive a natural parallel variant, qNEHVI, that reduces computational complexity of parallel EHVI from exponential to polynomial with respect to the batch size.

This is the distribution over datasets one obtains by first sampling a task t from Pt, and then sampling a dataset S from Pmz|t. Here p(S) corresponds to the marginal distribution over datasets S. Note that the last line above holds because E P f(,S) does not depend on t. Thus, in this section, we present a specialization of the bound for Gaussian distributions. Let P have mean µ and covariance; thus P = N(µ,) and analogously P,0 = N(µ0, 0). We can then apply the analytical form for the KL-divergence between two multivariate Gaussian distributions to the bound presented in Theorem 3. The result is the following bound holding under the same assumptions as Theorem 3: L(P,Pt) 1 l We implement the above bound in code instead of the non-specialized form of the KL divergence to speed up computations and simplify gradient computations. A.3.2 Few-Shot Learning Bound with Validation Data In this section, we will assume that, in addition to the training data S Pmz|t, we have access to validation data Sva Pnz|t at meta-training time. We will show that a meta-learning generalization bound can still be obtained in this case.

We are motivated by the problem of providing strong generalization guarantees in the context of meta-learning. Existing generalization bounds are either challenging to evaluate or provide vacuous guarantees in even relatively simple settings. We derive a probably approximately correct (PAC) bound for gradient-based metalearning using two different generalization frameworks in order to deal with the qualitatively different challenges of generalization at the "base" and "meta" levels. We employ bounds for uniformly stable algorithms at the base level and bounds from the PAC-Bayes framework at the meta level. The result of this approach is a novel PAC bound that is tighter when the base learner adapts quickly, which is precisely the goal of meta-learning. We show that our bound provides a tighter guarantee than other bounds on a toy non-convex problem on the unit sphere and a text-based classification example. We also present a practical regularization scheme motivated by the bound in settings where the bound is loose and demonstrate improved performance over baseline techniques.

A.1 Notation Let T be a failure time with CDFF. T's survival function is defined by F = 1 F. We denote failure models by FθT. Let C be a censoring time with CDFG, survival function G, and model GθC. Under right-censoring, define U = min(T,C), = 1 [T C] and we observe (Xi,Ui, i). We use G(t) to denote P(C t).

What spatial frequency information do humans and neural networks use to recognize objects? In neuroscience, critical band masking is an established tool that can reveal the frequency-selective filters used for object recognition. Critical band masking measures the sensitivity of recognition performance to noise added at each spatial frequency. Existing critical band masking studies show that humans recognize periodic patterns (gratings) and letters by means of a spatial-frequency filter (or "channel") that has a frequency bandwidth of one octave (doubling of frequency). Here, we introduce critical band masking as a task for network-human comparison and test 14 humans and 76 neural networks on 16-way ImageNet categorization in the presence of narrowband noise.