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This study addresses the challenge of fleet design optimization in the context of heterogeneous multi-robot fleets, aiming to obtain feasible designs that balance performance and costs. In the domain of autonomous multi-robot exploration, reinforcement learning agents play a central role, offering adaptability to complex terrains and facilitating collaboration among robots. However, modifying the fleet composition results in changes in the learned behavior, and training multi-robot systems using multi-agent reinforcement learning is expensive. Therefore, an exhaustive evaluation of each potential fleet design is infeasible. To tackle these hurdles, we introduce Bayesian Optimization for Fleet Design (BOFD), a framework leveraging multi-objective Bayesian Optimization to explore fleets on the Pareto front of performance and cost while accounting for uncertainty in the design space. Moreover, we establish a sub-linear bound for cumulative regret, supporting BOFD's robustness and efficacy. Extensive benchmark experiments in synthetic and simulated environments demonstrate the superiority of our framework over state-of-the-art methods, achieving efficient fleet designs with minimal fleet evaluations.

We introduce a novel problem setting for algorithmic contract design, named the principal-MARL contract design problem. This setting extends traditional contract design to account for dynamic and stochastic environments using Markov Games and Multi-Agent Reinforcement Learning. To tackle this problem, we propose a Multi-Objective Bayesian Optimization (MOBO) framework named Constrained Pareto Maximum Entropy Search (cPMES). Our approach integrates MOBO and MARL to explore the highly constrained contract design space, identifying promising incentive and recruitment decisions. cPMES transforms the principal-MARL contract design problem into an unconstrained multi-objective problem, leveraging the probability of feasibility as part of the objectives and ensuring promising designs predicted on the feasibility border are included in the Pareto front. By focusing the entropy prediction on designs within the Pareto set, cPMES mitigates the risk of the search strategy being overwhelmed by entropy from constraints. We demonstrate the effectiveness of cPMES through extensive benchmark studies in synthetic and simulated environments, showing its ability to find feasible contract designs that maximize the principal's objectives. Additionally, we provide theoretical support with a sub-linear regret bound concerning the number of iterations.

Learning a new task from a handful of examples remains an open challenge in machine learning. Despite the recent progress in few-shot learning, most methods rely on supervised pretraining or meta-learning on labeled meta-training data and cannot be applied to the case where the pretraining data is unlabeled. In this study, we present an unsupervised few-shot learning method via deep Laplacian eigenmaps. Our method learns representation from unlabeled data by grouping similar samples together and can be intuitively interpreted by random walks on augmented training data. We analytically show how deep Laplacian eigenmaps avoid collapsed representation in unsupervised learning without explicit comparison between positive and negative samples. The proposed method significantly closes the performance gap between supervised and unsupervised few-shot learning. Our method also achieves comparable performance to current state-of-the-art self-supervised learning methods under linear evaluation protocol.

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of dimensionality in new ways. However, deep learning methods are constrained by training time and memory. To tackle these shortcomings, we implement Tensor Neural Networks (TNN), a quantum-inspired neural network architecture that leverages Tensor Network ideas to improve upon deep learning approaches. We demonstrate that TNN provide significant parameter savings while attaining the same accuracy as compared to the classical Dense Neural Network (DNN). In addition, we also show how TNN can be trained faster than DNN for the same accuracy. We benchmark TNN by applying them to solve parabolic PDEs, specifically the Black-Scholes-Barenblatt equation, widely used in financial pricing theory, empirically showing the advantages of TNN over DNN. Further examples, such as the Hamilton-Jacobi-Bellman equation, are also discussed., Comment: 14 pages, 11 figures, minimal changes

Time series observations can be seen as realizations of an underlying dynamical system governed by rules that we typically do not know. For time series learning tasks, we need to understand that we fit our model on available data, which is a unique realized history. Training on a single realization often induces severe overfitting lacking generalization. To address this issue, we introduce a general recursive framework for time series augmentation, which we call Recursive Interpolation Method, denoted as RIM. New samples are generated using a recursive interpolation function of all previous values in such a way that the enhanced samples preserve the original inherent time series dynamics. We perform theoretical analysis to characterize the proposed RIM and to guarantee its test performance. We apply RIM to diverse real world time series cases to achieve strong performance over non-augmented data on regression, classification, and reinforcement learning tasks., Comment: Accepted to ICLR 2023 Resubmitted here due to major change in proofs following conference submission

Recent studies on few-shot classification using transfer learning pose challenges to the effectiveness and efficiency of episodic meta-learning algorithms. Transfer learning approaches are a natural alternative, but they are restricted to few-shot classification. Moreover, little attention has been on the development of probabilistic models with well-calibrated uncertainty from few-shot samples, except for some Bayesian episodic learning algorithms. To tackle the aforementioned issues, we propose a new transfer learning method to obtain accurate and reliable models for few-shot regression and classification. The resulting method does not require episodic meta-learning and is called meta-free representation learning (MFRL). MFRL first finds low-rank representation generalizing well on meta-test tasks. Given the learned representation, probabilistic linear models are fine-tuned with few-shot samples to obtain models with well-calibrated uncertainty. The proposed method not only achieves the highest accuracy on a wide range of few-shot learning benchmark datasets but also correctly quantifies the prediction uncertainty. In addition, weight averaging and temperature scaling are effective in improving the accuracy and reliability of few-shot learning in existing meta-learning algorithms with a wide range of learning paradigms and model architectures.