We present Myriad, a testbed written in JAX for learning and planning in real-world continuous environments. The primary contributions of Myriad are threefold. First, Myriad provides machine learning practitioners access to trajectory optimization techniques for application within a typical automatic differentiation workflow. Second, Myriad presents many real-world optimal control problems, ranging from biology to medicine to engineering, for use by the machine learning community. Formulated in continuous space and time, these environments retain some of the complexity of real-world systems often abstracted away by standard benchmarks. As such, Myriad strives to serve as a stepping stone towards application of modern machine learning techniques for impactful real-world tasks. Finally, we use the Myriad repository to showcase a novel approach for learning and control tasks. Trained in a fully end-to-end fashion, our model leverages an implicit planning module over neural ordinary differential equations, enabling simultaneous learning and planning with complex environment dynamics.

Distributed optimization provides a framework for deriving distributed algorithms for a variety of multi-robot problems. This tutorial constitutes the first part of a two-part series on distributed optimization applied to multi-robot problems, which seeks to advance the application of distributed optimization in robotics. In this tutorial, we demonstrate that many canonical multi-robot problems can be cast within the distributed optimization framework, such as multi-robot simultaneous localization and planning (SLAM), multi-robot target tracking, and multi-robot task assignment problems. We identify three broad categories of distributed optimization algorithms: distributed first-order methods, distributed sequential convex programming, and the alternating direction method of multipliers (ADMM). We describe the basic structure of each category and provide representative algorithms within each category. We then work through a simulation case study of multiple drones collaboratively tracking a ground vehicle. We compare solutions to this problem using a number of different distributed optimization algorithms. In addition, we implement a distributed optimization algorithm in hardware on a network of Rasberry Pis communicating with XBee modules to illustrate robustness to the challenges of real-world communication networks.

Real-time machine learning has recently attracted significant interest due to its potential to support instantaneous learning, adaptation, and decision making in a wide range of application domains, including self-driving vehicles, intelligent transportation, and industry automation. We investigate real-time ML in a federated edge intelligence (FEI) system, an edge computing system that implements federated learning (FL) solutions based on data samples collected and uploaded from decentralized data networks. FEI systems often exhibit heterogenous communication and computational resource distribution, as well as non-i.i.d. data samples, resulting in long model training time and inefficient resource utilization. Motivated by this fact, we propose a time-sensitive federated learning (TS-FL) framework to minimize the overall run-time for collaboratively training a shared ML model. Training acceleration solutions for both TS-FL with synchronous coordination (TS-FL-SC) and asynchronous coordination (TS-FL-ASC) are investigated. To address straggler effect in TS-FL-SC, we develop an analytical solution to characterize the impact of selecting different subsets of edge servers on the overall model training time. A server dropping-based solution is proposed to allow slow-performance edge servers to be removed from participating in model training if their impact on the resulting model accuracy is limited. A joint optimization algorithm is proposed to minimize the overall time consumption of model training by selecting participating edge servers, local epoch number. We develop an analytical expression to characterize the impact of staleness effect of asynchronous coordination and straggler effect of FL on the time consumption of TS-FL-ASC. Experimental results show that TS-FL-SC and TS-FL-ASC can provide up to 63% and 28% of reduction, in the overall model training time, respectively.

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics (Li et al., 2020) and follows an incremental learning procedure (Gissin et al., 2019): GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.

Advances in machine learning have enabled the prediction of immune system responses to prophylactic and therapeutic vaccines. However, the engineering task of designing vaccines remains a challenge. In particular, the genetic variability of the human immune system makes it difficult to design peptide vaccines that provide widespread immunity in vaccinated populations. We introduce a framework for evaluating and designing peptide vaccines that uses probabilistic machine learning models, and demonstrate its ability to produce designs for a SARS-CoV-2 vaccine that outperform previous designs. We provide a theoretical analysis of the approximability, scalability, and complexity of our framework.

In this work, we consider learning sparse models in large scale settings, where the number of samples and the feature dimension can grow as large as millions or billions. Two immediate issues occur under such challenging scenario: (i) computational cost; (ii) memory overhead. In particular, the memory issue precludes a large volume of prior algorithms that are based on batch optimization technique. To remedy the problem, we propose to learn sparse models such as Lasso in an online manner where in each iteration, only one randomly chosen sample is revealed to update a sparse iterate. Thereby, the memory cost is independent of the sample size and gradient evaluation for one sample is efficient. Perhaps amazingly, we find that with the same parameter, sparsity promoted by batch methods is not preserved in online fashion. We analyze such interesting phenomenon and illustrate some effective variants including mini-batch methods and a hard thresholding based stochastic gradient algorithm. Extensive experiments are carried out on a public dataset which supports our findings and algorithms.

Conventional rule learning algorithms aim at finding a set of simple rules, where each rule covers as many examples as possible. In this paper, we argue that the rules found in this way may not be the optimal explanations for each of the examples they cover. Instead, we propose an efficient algorithm that aims at finding the best rule covering each training example in a greedy optimization consisting of one specialization and one generalization loop. These locally optimal rules are collected and then filtered for a final rule set, which is much larger than the sets learned by conventional rule learning algorithms. A new example is classified by selecting the best among the rules that cover this example. In our experiments on small to very large datasets, the approach's average classification accuracy is higher than that of state-of-the-art rule learning algorithms. Moreover, the algorithm is highly efficient and can inherently be processed in parallel without affecting the learned rule set and so the classification accuracy. We thus believe that it closes an important gap for large-scale classification rule induction.

Although the field of distributed optimization is well-developed, relevant literature focused on the application of distributed optimization to multi-robot problems is limited. This survey constitutes the second part of a two-part series on distributed optimization applied to multi-robot problems. In this paper, we survey three main classes of distributed optimization algorithms -- distributed first-order methods, distributed sequential convex programming methods, and alternating direction method of multipliers (ADMM) methods -- focusing on fully-distributed methods that do not require coordination or computation by a central computer. We describe the fundamental structure of each category and note important variations around this structure, designed to address its associated drawbacks. Further, we provide practical implications of noteworthy assumptions made by distributed optimization algorithms, noting the classes of robotics problems suitable for these algorithms. Moreover, we identify important open research challenges in distributed optimization, specifically for robotics problem.

We study the sample complexity of reducing reinforcement learning to a sequence of empirical risk minimization problems over the policy space. Such reductions-based algorithms exhibit local convergence in the function space, as opposed to the parameter space for policy gradient algorithms, and thus are unaffected by the possibly non-linear or discontinuous parameterization of the policy class. We propose a variance-reduced variant of Conservative Policy Iteration that improves the sample complexity of producing a $\varepsilon$-functional local optimum from $O(\varepsilon^{-4})$ to $O(\varepsilon^{-3})$. Under state-coverage and policy-completeness assumptions, the algorithm enjoys $\varepsilon$-global optimality after sampling $O(\varepsilon^{-2})$ times, improving upon the previously established $O(\varepsilon^{-3})$ sample requirement.

We study the random reshuffling (RR) method for smooth nonconvex optimization problems with a finite-sum structure. Though this method is widely utilized in practice such as the training of neural networks, its convergence behavior is only understood in several limited settings. In this paper, under the well-known Kurdyka-Lojasiewicz (KL) inequality, we establish strong limit-point convergence results for RR with appropriate diminishing step sizes, namely, the whole sequence of iterates generated by RR is convergent and converges to a single stationary point in an almost sure sense. In addition, we derive the corresponding rate of convergence, depending on the KL exponent and the suitably selected diminishing step sizes. When the KL exponent lies in $[0,\frac12]$, the convergence is at a rate of $\mathcal{O}(t^{-1})$ with $t$ counting the iteration number. When the KL exponent belongs to $(\frac12,1)$, our derived convergence rate is of the form $\mathcal{O}(t^{-q})$ with $q\in (0,1)$ depending on the KL exponent. The standard KL inequality-based convergence analysis framework only applies to algorithms with a certain descent property. We conduct a novel convergence analysis for the non-descent RR method with diminishing step sizes based on the KL inequality, which generalizes the standard KL framework. We summarize our main steps and core ideas in an informal analysis framework, which is of independent interest. As a direct application of this framework, we also establish similar strong limit-point convergence results for the reshuffled proximal point method.