We consider probabilistic models for sequential observations which exhibit gradual transitions among a finite number of states. We are particularly motivated by applications such as human activity analysis where observed accelerometer time series contains segments representing distinct activities, which we call pure states, as well as periods characterized by continuous transition among these pure states. To capture this transitory behavior, the dynamical Wasserstein barycenter (DWB) model of [1] associates with each pure state a data-generating distribution and models the continuous transitions among these states as a Wasserstein barycenter of these distributions with dynamically evolving weights. Focusing on the univariate case where Wasserstein distances and barycenters can be computed in closed form, we extend [1] specifically relaxing the parameterization of the pure states as Gaussian distributions. We highlight issues related to the uniqueness in identifying the model parameters as well as uncertainties induced when estimating a dynamically evolving distribution from a limited number of samples. To ameliorate non-uniqueness, we introduce regularization that imposes temporal smoothness on the dynamics of the barycentric weights. A quantile-based approximation of the pure state distributions yields a finite dimensional estimation problem which we numerically solve using cyclic descent alternating between updates to the pure-state quantile functions and the barycentric weights. We demonstrate the utility of the proposed algorithm in segmenting both simulated and real world human activity time series. We consider a probabilistic model for sequentially observed data where the observation at each point in time depends on a dynamically evolving latent state. We are particularly motivated by systems that continuously move among a set of canonical behaviors, which we call pure states.

A common formulation of constrained reinforcement learning involves multiple rewards that must individually accumulate to given thresholds. In this class of problems, we show a simple example in which the desired optimal policy cannot be induced by any weighted linear combination of rewards. Hence, there exist constrained reinforcement learning problems for which neither regularized nor classical primal-dual methods yield optimal policies. This work addresses this shortcoming by augmenting the state with Lagrange multipliers and reinterpreting primal-dual methods as the portion of the dynamics that drives the multipliers evolution. This approach provides a systematic state augmentation procedure that is guaranteed to solve reinforcement learning problems with constraints. Thus, as we illustrate by an example, while previous methods can fail at finding optimal policies, running the dual dynamics while executing the augmented policy yields an algorithm that provably samples actions from the optimal policy.

Consider an online convex optimization problem where the loss functions are self-concordant barriers, smooth relative to a convex function $h$, and possibly non-Lipschitz. We analyze the regret of online mirror descent with $h$. Then, based on the result, we prove the following in a unified manner. Denote by $T$ the time horizon and $d$ the parameter dimension. 1. For online portfolio selection, the regret of $\widetilde{\text{EG}}$, a variant of exponentiated gradient due to Helmbold et al., is $\tilde{O} ( T^{2/3} d^{1/3} )$ when $T > 4 d / \log d$. This improves on the original $\tilde{O} ( T^{3/4} d^{1/2} )$ regret bound for $\widetilde{\text{EG}}$. 2. For online portfolio selection, the regret of online mirror descent with the logarithmic barrier is $\tilde{O}(\sqrt{T d})$. The regret bound is the same as that of Soft-Bayes due to Orseau et al. up to logarithmic terms. 3. For online learning quantum states with the logarithmic loss, the regret of online mirror descent with the log-determinant function is also $\tilde{O} ( \sqrt{T d} )$. Its per-iteration time is shorter than all existing algorithms we know.

Emerging real-time multi-model ML (RTMM) workloads such as AR/VR and drone control involve dynamic behaviors in various granularity; task, model, and layers within a model. Such dynamic behaviors introduce new challenges to the system software in an ML system since the overall system load is not completely predictable, unlike traditional ML workloads. In addition, RTMM workloads require real-time processing, involve highly heterogeneous models, and target resource-constrained devices. Under such circumstances, developing an effective scheduler gains more importance to better utilize underlying hardware considering the unique characteristics of RTMM workloads. Therefore, we propose a new scheduler, DREAM, which effectively handles various dynamicity in RTMM workloads targeting multi-accelerator systems. DREAM quantifies the unique requirements for RTMM workloads and utilizes the quantified scores to drive scheduling decisions, considering the current system load and other inference jobs on different models and input frames. DREAM utilizes tunable parameters that provide fast and effective adaptivity to dynamic workload changes. In our evaluation of five scenarios of RTMM workload, DREAM reduces the overall UXCost, which is an equivalent metric of the energy-delay product (EDP) for RTMM defined in the paper, by 32.2% and 50.0% in the geometric mean (up to 80.8% and 97.6%) compared to state-of-the-art baselines, which shows the efficacy of our scheduling methodology.

Cloth manipulation is a category of deformable object manipulation of great interest to the robotics community, from applications of automated laundry-folding and home organizing and cleaning to textiles and flexible manufacturing. Despite the desire for automated cloth manipulation, the thin-shell dynamics and under-actuation nature of cloth present significant challenges for robots to effectively interact with them. Many recent works omit explicit modeling in favor of learning-based methods that may yield control policies directly. However, these methods require large training sets that must be collected and curated. In this regard, we create a framework for differentiable modeling of cloth dynamics leveraging an Extended Position-based Dynamics (XPBD) algorithm. Together with the desired control objective, physics-aware regularization terms are designed for better results, including trajectory smoothness and elastic potential energy. In addition, safety constraints, such as avoiding obstacles, can be specified using signed distance functions (SDFs). We formulate the cloth manipulation task with safety constraints as a constrained optimization problem, which can be effectively solved by mainstream gradient-based optimizers thanks to the end-to-end differentiability of our framework. Finally, we assess the proposed framework for manipulation tasks with various safety thresholds and demonstrate the feasibility of result trajectories on a surgical robot. The effects of the regularization terms are analyzed in an additional ablation study.

Federated Learning (FL) is a distributed machine learning approach that enables model training in communication efficient and privacy-preserving manner. The standard optimization method in FL is Federated Averaging (FedAvg), which performs multiple local SGD steps between communication rounds. FedAvg has been considered to lack algorithm adaptivity compared to modern first-order adaptive optimizations. In this paper, we propose new communication-efficient FL algortithms based on two adaptive frameworks: local adaptivity (PreFed) and server-side adaptivity (PreFedOp). Proposed methods adopt adaptivity by using a novel covariance matrix preconditioner. Theoretically, we provide convergence guarantees for our algorithms. The empirical experiments show our methods achieve state-of-the-art performances on both i.i.d. and non-i.i.d. settings.

This paper studies the problem of online performance optimization of constrained closed-loop control systems, where both the objective and the constraints are unknown black-box functions affected by exogenous time-varying contextual disturbances. A primal-dual contextual Bayesian optimization algorithm is proposed that achieves sublinear cumulative regret with respect to the dynamic optimal solution under certain regularity conditions. Furthermore, the algorithm achieves zero time-average constraint violation, ensuring that the average value of the constraint function satisfies the desired constraint. The method is applied to both sampled instances from Gaussian processes and a continuous stirred tank reactor parameter tuning problem; simulation results show that the method simultaneously provides close-to-optimal performance and maintains constraint feasibility on average. This contrasts current state-of-the-art methods, which either suffer from large cumulative regret or severe constraint violations for the case studies presented.

While training fair machine learning models has been studied extensively in recent years, most developed methods rely on the assumption that the training and test data have similar distributions. In the presence of distribution shifts, fair models may behave unfairly on test data. There have been some developments for fair learning robust to distribution shifts to address this shortcoming. However, most proposed solutions are based on the assumption of having access to the causal graph describing the interaction of different features. Moreover, existing algorithms require full access to data and cannot be used when small batches are used (stochastic/batch implementation). This paper proposes the first stochastic distributionally robust fairness framework with convergence guarantees that do not require knowledge of the causal graph. More specifically, we formulate the fair inference in the presence of the distribution shift as a distributionally robust optimization problem under $L_p$ norm uncertainty sets with respect to the Exponential Renyi Mutual Information (ERMI) as the measure of fairness violation. We then discuss how the proposed method can be implemented in a stochastic fashion. We have evaluated the presented framework's performance and efficiency through extensive experiments on real datasets consisting of distribution shifts.

We examine a stochastic formulation for data-driven optimization wherein the decision-maker is not privy to the true distribution, but has knowledge that it lies in some hypothesis set and possesses a historical data set, from which information about it can be gleaned. We define a prescriptive solution as a decision rule mapping such a data set to decisions. As there does not exist prescriptive solutions that are generalizable over the entire hypothesis set, we define out-of-sample optimality as a local average over a neighbourhood of hypotheses, and averaged over the sampling distribution. We prove sufficient conditions for local out-of-sample optimality, which reduces to functions of the sufficient statistic of the hypothesis family. We present an optimization problem that would solve for such an out-of-sample optimal solution, and does so efficiently by a combination of sampling and bisection search algorithms. Finally, we illustrate our model on the newsvendor model, and find strong performance when compared against alternatives in the literature. There are potential implications of our research on end-to-end learning and Bayesian optimization.

Fleets of unmanned robots can be beneficial for the long-term monitoring of large areas, e.g., to monitor wild flocks, detect intruders, search and rescue. Monitoring numerous dynamic targets in a collaborative and efficient way is a challenging problem that requires online coordination and information fusion. The majority of existing works either assume a passive all-to-all observation model to minimize the summed uncertainties over all targets by all robots, or optimize over the jointed discrete actions while neglecting the dynamic constraints of the robots and unknown behaviors of the targets. This work proposes an online task and motion coordination algorithm that ensures an explicitly-bounded estimation uncertainty for the target states, while minimizing the average number of active robots. The robots have a limited-range perception to actively track a limited number of targets simultaneously, of which their future control decisions are all unknown. It includes: (i) the assignment of monitoring tasks, modeled as a flexible size multiple vehicle routing problem with time windows (m-MVRPTW), given the predicted target trajectories with uncertainty measure in the road-networks; (ii) the nonlinear model predictive control (NMPC) for optimizing the robot trajectories under uncertainty and safety constraints. It is shown that the robots can switch between active and inactive roles dynamically online as required by the unknown monitoring task. The proposed methods are validated via large-scale simulations of up to $100$ robots and targets.