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This paper proposes an inverse optimal control method which enables a robot to incrementally learn a control objective function from a collection of trajectory segments. By saying incrementally, it means that the collection of trajectory segments is enlarged because additional segments are provided as time evolves. The unknown objective function is parameterized as a weighted sum of features with unknown weights. Each trajectory segment is a small snippet of optimal trajectory. The proposed method shows that each trajectory segment, if informative, can pose a linear constraint to the unknown weights, thus, the objective function can be learned by incrementally incorporating all informative segments. Effectiveness of the method is shown on a simulated 2-link robot arm and a 6-DoF maneuvering quadrotor system, in each of which only small demonstration segments are available.

We study the problem of multi-agent control of a dynamical system with known dynamics and adversarial disturbances. Our study focuses on optimal control without centralized precomputed policies, but rather with adaptive control policies for the different agents that are only equipped with a stabilizing controller. We give a reduction from any (standard) regret minimizing control method to a distributed algorithm. The reduction guarantees that the resulting distributed algorithm has low regret relative to the optimal precomputed joint policy. Our methodology involves generalizing online convex optimization to a multi-agent setting and applying recent tools from nonstochastic control derived for a single agent. We empirically evaluate our method on a model of an overactuated aircraft. We show that the distributed method is robust to failure and to adversarial perturbations in the dynamics.

In DP-SGD each round communicates a local SGD update which leaks some new information about the underlying local data set to the outside world. In order to provide privacy, Gaussian noise with standard deviation $\sigma$ is added to local SGD updates after performing a clipping operation. We show that for attaining $(\epsilon,\delta)$-differential privacy $\sigma$ can be chosen equal to $\sqrt{2(\epsilon +\ln(1/\delta))/\epsilon}$ for $\epsilon=\Omega(T/N^2)$, where $T$ is the total number of rounds and $N$ is equal to the size of the local data set. In many existing machine learning problems, $N$ is always large and $T=O(N)$. Hence, $\sigma$ becomes "independent" of any $T=O(N)$ choice with $\epsilon=\Omega(1/N)$. This means that our $\sigma$ only depends on $N$ rather than $T$. As shown in our paper, this differential privacy characterization allows one to {\it a-priori} select parameters of DP-SGD based on a fixed privacy budget (in terms of $\epsilon$ and $\delta$) in such a way to optimize the anticipated utility (test accuracy) the most. This ability of planning ahead together with $\sigma$'s independence of $T$ (which allows local gradient computations to be split among as many rounds as needed, even for large $T$ as usually happens in practice) leads to a {\it proactive DP-SGD algorithm} that allows a client to balance its privacy budget with the accuracy of the learned global model based on local test data. We notice that the current state-of-the art differential privacy accountant method based on $f$-DP has a closed form for computing the privacy loss for DP-SGD. However, due to its interpretation complexity, it cannot be used in a simple way to plan ahead. Instead, accountant methods are only used for keeping track of how privacy budget has been spent (after the fact).

In recent years, the literature on Bayesian high-dimensional variable selection has rapidly grown. It is increasingly important to understand whether these Bayesian methods can consistently estimate the model parameters. To this end, shrinkage priors are useful for identifying relevant signals in high-dimensional data. For multivariate linear regression models with Gaussian response variables, Bai and Ghosh (2018) proposed a multivariate Bayesian model with shrinkage priors (MBSP) for estimation and variable selection in high-dimensional settings. However, the proofs of posterior consistency for the MBSP method (Theorems 3 and 4 of Bai and Ghosh (2018) were incorrect. In this paper, we provide a corrected proof of Theorems 3 and 4 of Bai and Ghosh (2018). We leverage these new proofs to extend the MBSP model to multivariate generalized linear models (GLMs). Under our proposed model (MBSP-GLM), multiple responses belonging to the exponential family are simultaneously modeled and mixed-type responses are allowed. We show that the MBSP-GLM model achieves strong posterior consistency when $p$ grows at a subexponential rate with $n$. Furthermore, we quantify the posterior contraction rate at which the posterior shrinks around the true regression coefficients and allow the dimension of the responses $q$ to grow as $n$ grows. Thus, we strengthen the previous results on posterior consistency, which did not provide rate results. This greatly expands the scope of the MBSP model to include response variables of many data types, including binary and count data. To the best of our knowledge, this is the first posterior contraction result for multivariate Bayesian GLMs.

While artificial-intelligence-based methods suffer from lack of transparency, rule-based methods dominate in safety-critical systems. Yet, the latter cannot compete with the first ones in robustness to multiple requirements, for instance, simultaneously addressing safety, comfort, and efficiency. Hence, to benefit from both methods they must be joined in a single system. This paper proposes a decision making and control framework, which profits from advantages of both the rule- and machine-learning-based techniques while compensating for their disadvantages. The proposed method embodies two controllers operating in parallel, called Safety and Learned. A rule-based switching logic selects one of the actions transmitted from both controllers. The Safety controller is prioritized every time, when the Learned one does not meet the safety constraint, and also directly participates in the safe Learned controller training. Decision making and control in autonomous driving is chosen as the system case study, where an autonomous vehicle learns a multi-task policy to safely cross an unprotected intersection. Multiple requirements (i.e., safety, efficiency, and comfort) are set for vehicle operation. A numerical simulation is performed for the proposed framework validation, where its ability to satisfy the requirements and robustness to changing environment is successfully demonstrated.

Driven by the fast development of Internet of Things (IoT) applications, tremendous data need to be collected by sensors and passed to the servers for further process. As a promising solution, the mobile crowd sensing (MCS) enables controllable sensing and transmission processes for multiple types of data in a single device. To achieve the energy efficient MCS, the data sensing and transmission over a long-term time duration should be designed accounting for the differentiated requirements of IoT tasks including data size and delay tolerance. The said design is achieved by jointly optimizing the sensing and transmission rates, which leads to a complex optimization problem due to the restraining relationship between the controlling variables as well as the existence of busy time interval during which no data can be sensed. To deal with such problem, a vital concept namely height is introduced, based on which the classical string-pulling algorithms can be applied for obtaining the corresponding optimal sensing and transmission rates. Therefore, the original rates optimization problem can be converted to a searching problem for the optimal height. Based on the property of the objective function, the upper and lower bounds of the area where the optimal height lies in are derived. The whole searching area is further divided into a series of sub-areas due to the format change of the objective function with the varying heights. Finally, the optimal height in each sub-area is obtained based on the convexity of the objective function and the global optimal height is further determined by comparing the local optimums. The above solving approach is further extended for the case with limited data buffer capacity of the server. Simulations are conducted to evaluate the performance of the proposed design.

In online learning problems, exploiting low variance plays an important role in obtaining tight performance guarantees yet is challenging because variances are often not known a priori. Recently, considerable progress has been made by Zhang et al. (2021) where they obtain a variance-adaptive regret bound for linear bandits without knowledge of the variances and a horizon-free regret bound for linear mixture Markov decision processes (MDPs). In this paper, we present novel analyses that improve their regret bounds significantly. For linear bandits, we achieve $\tilde O(d^{1.5}\sqrt{\sum_{k}^K \sigma_k^2} + d^2)$ where $d$ is the dimension of the features, $K$ is the time horizon, and $\sigma_k^2$ is the noise variance at time step $k$, and $\tilde O$ ignores polylogarithmic dependence, which is a factor of $d^3$ improvement. For linear mixture MDPs with the assumption of maximum cumulative reward in an episode being in $[0,1]$, we achieve a horizon-free regret bound of $\tilde O(d \sqrt{K} + d^2)$ where $d$ is the number of base models and $K$ is the number of episodes. This is a factor of $d^{3.5}$ improvement in the leading term and $d^7$ in the lower order term. Our analysis critically relies on a novel elliptical potential `count' lemma. This lemma allows a novel regret analysis in conjunction with the peeling trick, which is of independent interest.

It is a consensus that small models perform quite poorly under the paradigm of self-supervised contrastive learning. Existing methods usually adopt a large off-the-shelf model to transfer knowledge to the small one via distillation. Despite their effectiveness, distillation-based methods may not be suitable for some resource-restricted scenarios due to the huge computational expenses of deploying a large model. In this paper, we study the issue of training self-supervised small models without distillation signals. We first evaluate the representation spaces of the small models and make two non-negligible observations: (i) the small models can complete the pretext task without overfitting despite their limited capacity and (ii) they universally suffer the problem of over clustering. Then we verify multiple assumptions that are considered to alleviate the over-clustering phenomenon. Finally, we combine the validated techniques and improve the baseline performances of five small architectures with considerable margins, which indicates that training small self-supervised contrastive models is feasible even without distillation signals. The code is available at \textit{//github.com/WOWNICE/ssl-small}.

Although reinforcement learning methods can achieve impressive results in simulation, the real world presents two major challenges: generating samples is exceedingly expensive, and unexpected perturbations can cause proficient but narrowly-learned policies to fail at test time. In this work, we propose to learn how to quickly and effectively adapt online to new situations as well as to perturbations. To enable sample-efficient meta-learning, we consider learning online adaptation in the context of model-based reinforcement learning. Our approach trains a global model such that, when combined with recent data, the model can be be rapidly adapted to the local context. Our experiments demonstrate that our approach can enable simulated agents to adapt their behavior online to novel terrains, to a crippled leg, and in highly-dynamic environments.