Several works have shown that perturbation stable instances of the MAP inference problem in Potts models can be solved exactly using a natural linear programming (LP) relaxation. However, most of these works give few (or no) guarantees for the LP solutions on instances that do not satisfy the relatively strict perturbation stability definitions. In this work, we go beyond these stability results by showing that the LP approximately recovers the MAP solution of a stable instance even after the instance is corrupted by noise. This "noisy stable" model realistically fits with practical MAP inference problems: we design an algorithm for finding "close" stable instances, and show that several real-world instances from computer vision have nearby instances that are perturbation stable. These results suggest a new theoretical explanation for the excellent performance of this LP relaxation in practice.

In this work we propose a batch Bayesian optimization method for combinatorial problems on permutations, which is well suited for expensive cost functions on permutations. We introduce LAW, a new efficient batch acquisition method based on the determinantal point process, using an acquisition weighted kernel. Relying on multiple parallel evaluations, LAW accelerates the search for the optimal permutation. We provide a regret analysis for our method to gain insight in its theoretical properties. We then apply the framework to permutation problems, which have so far received little attention in the Bayesian Optimization literature, despite their practical importance. We call this method LAW2ORDER. We evaluate the method on several standard combinatorial problems involving permutations such as quadratic assignment, flowshop scheduling and the traveling salesman, as well as on a structure learning task.

Energy harvesting offers an attractive and promising mechanism to power low-energy devices. However, it alone is insufficient to enable an energy-neutral operation, which can eliminate tedious battery charging and replacement requirements. Achieving an energy-neutral operation is challenging since the uncertainties in harvested energy undermine the quality of service requirements. To address this challenge, we present a rollout-based runtime energy-allocation framework that optimizes the utility of the target device under energy constraints. The proposed framework uses an efficient iterative algorithm to compute initial energy allocations at the beginning of a day. The initial allocations are then corrected at every interval to compensate for the deviations from the expected energy harvesting pattern. We evaluate this framework using solar and motion energy harvesting modalities and American Time Use Survey data from 4772 different users. Compared to state-of-the-art techniques, the proposed framework achieves 34.6% higher utility even under energy-limited scenarios. Moreover, measurements on a wearable device prototype show that the proposed framework has less than 0.1% energy overhead compared to iterative approaches with a negligible loss in utility.

Missing time-series data is a prevalent practical problem. Imputation methods in time-series data often are applied to the full panel data with the purpose of training a model for a downstream out-of-sample task. For example, in finance, imputation of missing returns may be applied prior to training a portfolio optimization model. Unfortunately, this practice may result in a look-ahead-bias in the future performance on the downstream task. There is an inherent trade-off between the look-ahead-bias of using the full data set for imputation and the larger variance in the imputation from using only the training data. By connecting layers of information revealed in time, we propose a Bayesian posterior consensus distribution which optimally controls the variance and look-ahead-bias trade-off in the imputation. We demonstrate the benefit of our methodology both in synthetic and real financial data.

Machine learning models are often implemented in cohort with humans in the pipeline, with the model having an option to defer to a domain expert in cases where it has low confidence in its inference. Our goal is to design mechanisms for ensuring accuracy and fairness in such prediction systems that combine machine learning model inferences and domain expert predictions. Prior work on "deferral systems" in classification settings has focused on the setting of a pipeline with a single expert and aimed to accommodate the inaccuracies and biases of this expert to simultaneously learn an inference model and a deferral system. Our work extends this framework to settings where multiple experts are available, with each expert having their own domain of expertise and biases. We propose a framework that simultaneously learns a classifier and a deferral system, with the deferral system choosing to defer to one or more human experts in cases of input where the classifier has low confidence. We test our framework on a synthetic dataset and a content moderation dataset with biased synthetic experts, and show that it significantly improves the accuracy and fairness of the final predictions, compared to the baselines. We also collect crowdsourced labels for the content moderation task to construct a real-world dataset for the evaluation of hybrid machine-human frameworks and show that our proposed learning framework outperforms baselines on this real-world dataset as well.

The sample efficiency of Bayesian optimization(BO) is often boosted by Gaussian Process(GP) surrogate models. However, on mixed variable spaces, surrogate models other than GPs are prevalent, mainly due to the lack of kernels which can model complex dependencies across different types of variables. In this paper, we propose the frequency modulated (FM) kernel flexibly modeling dependencies among different types of variables, so that BO can enjoy the further improved sample efficiency. The FM kernel uses distances on continuous variables to modulate the graph Fourier spectrum derived from discrete variables. However, the frequency modulation does not always define a kernel with the similarity measure behavior which returns higher values for pairs of more similar points. Therefore, we specify and prove conditions for FM kernels to be positive definite and to exhibit the similarity measure behavior. In experiments, we demonstrate the improved sample efficiency of GP BO using FM kernels (BO-FM).On synthetic problems and hyperparameter optimization problems, BO-FM outperforms competitors consistently. Also, the importance of the frequency modulation principle is empirically demonstrated on the same problems. On joint optimization of neural architectures and SGD hyperparameters, BO-FM outperforms competitors including Regularized evolution(RE) and BOHB. Remarkably, BO-FM performs better even than RE and BOHB using three times as many evaluations.

Sample code for hyper-parameter optimization implementation for machine learning algorithms is provided in this repository.

An Evolutionary Algorithm (EA) is a subset of evolutionary computation in artificial intelligence. Evolutionary computation is a family of algorithms for global optimization inspired by biological evolution. The rapid development of the information age with Big Data has led to an increase in the size and complexity of the optimization problems. In the context of an EA, this eventually results in the expansion of the search space with the fitness evaluation (used for optimal solution search) computation cost of the individuals becoming extremely high [1]. In this article, we will mainly focus on the Parallel EA variant with its two types and then dive deep into understanding the problem of evaluation time-bias.

In this paper, we study communication efficient distributed algorithms for distributionally robust federated learning via periodic averaging with adaptive sampling. In contrast to standard empirical risk minimization, due to the minimax structure of the underlying optimization problem, a key difficulty arises from the fact that the global parameter that controls the mixture of local losses can only be updated infrequently on the global stage. To compensate for this, we propose a Distributionally Robust Federated Averaging (DRFA) algorithm that employs a novel snapshotting scheme to approximate the accumulation of history gradients of the mixing parameter. We analyze the convergence rate of DRFA in both convex-linear and nonconvex-linear settings. We also generalize the proposed idea to objectives with regularization on the mixture parameter and propose a proximal variant, dubbed as DRFA-Prox, with provable convergence rates. We also analyze an alternative optimization method for regularized cases in strongly-convex-strongly-concave and non-convex (under PL condition)-strongly-concave settings. To the best of our knowledge, this paper is the first to solve distributionally robust federated learning with reduced communication, and to analyze the efficiency of local descent methods on distributed minimax problems. We give corroborating experimental evidence for our theoretical results in federated learning settings.

The widespread proliferation of data-driven decision-making has ushered in a recent interest in the design of privacy-preserving algorithms. In this paper, we consider the ubiquitous problem of gaussian process (GP) bandit optimization from the lens of privacy-preserving statistics. We propose a solution for differentially private GP bandit optimization that combines a uniform kernel approximator with random perturbations, providing a generic framework to create differentially-private (DP) Gaussian process bandit algorithms. For two specific DP settings - joint and local differential privacy, we provide algorithms based on efficient quadrature Fourier feature approximators, that are computationally efficient and provably no-regret for popular stationary kernel functions. Our algorithms maintain differential privacy throughout the optimization procedure and critically do not rely explicitly on the sample path for prediction, making the parameters straightforward to release as well.