A central task in control theory, artificial intelligence, and formal methods is to synthesize reward-maximizing strategies for agents that operate in partially unknown environments. In environments modeled by gray-box Markov decision processes (MDPs), the impact of the agents' actions are known in terms of successor states but not the stochastics involved. In this paper, we devise a strategy synthesis algorithm for gray-box MDPs via reinforcement learning that utilizes interval MDPs as internal model. To compete with limited sampling access in reinforcement learning, we incorporate two novel concepts into our algorithm, focusing on rapid and successful learning rather than on stochastic guarantees and optimality: lower confidence bound exploration reinforces variants of already learned practical strategies and action scoping reduces the learning action space to promising actions. We illustrate benefits of our algorithms by means of a prototypical implementation applied on examples from the AI and formal methods communities.
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Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to second-order methods that are computationally more expensive. In this work we aim to approximate a nonlinear model with a linear one and correct the resulting approximation error. We develop a sequential method that iteratively solves a linear inverse problem and updates the approximation error by evaluating it at the new solution. This treatment convexifies the problem and allows us to benefit from established convex optimization methods. We separately consider cases where the approximation is fixed over iterations and where the approximation is adaptive. In the fixed case we show theoretically under what assumptions the sequence converges. In the adaptive case, particularly considering the special case of approximation by first-order Taylor expansion, we show that with certain assumptions the sequence converges to a critical point of the original nonconvex functional. Furthermore, we show that with quadratic objective functions the sequence corresponds to the Gauss-Newton method. Finally, we showcase numerical results superior to the conventional model correction method. We also show, that a fixed approximation can provide competitive results with considerable computational speed-up.
Transformers have achieved superior performances in many tasks in natural language processing and computer vision, which also triggered great interest in the time series community. Among multiple advantages of Transformers, the ability to capture long-range dependencies and interactions is especially attractive for time series modeling, leading to exciting progress in various time series applications. In this paper, we systematically review Transformer schemes for time series modeling by highlighting their strengths as well as limitations. In particular, we examine the development of time series Transformers in two perspectives. From the perspective of network structure, we summarize the adaptations and modifications that have been made to Transformers in order to accommodate the challenges in time series analysis. From the perspective of applications, we categorize time series Transformers based on common tasks including forecasting, anomaly detection, and classification. Empirically, we perform robust analysis, model size analysis, and seasonal-trend decomposition analysis to study how Transformers perform in time series. Finally, we discuss and suggest future directions to provide useful research guidance. To the best of our knowledge, this paper is the first work to comprehensively and systematically summarize the recent advances of Transformers for modeling time series data. We hope this survey will ignite further research interests in time series Transformers.
In robotics, simulation has the potential to reduce design time and costs, and lead to a more robust engineered solution and a safer development process. However, the use of simulators is predicated on the availability of good models. This contribution is concerned with improving the quality of these models via calibration, which is cast herein in a Bayesian framework. First, we discuss the Bayesian machinery involved in model calibration. Then, we demonstrate it in one example: calibration of a vehicle dynamics model that has low degree of freedom count and can be used for state estimation, model predictive control, or path planning. A high fidelity simulator is used to emulate the ``experiments'' and generate the data for the calibration. The merit of this work is not tied to a new Bayesian methodology for calibration, but to the demonstration of how the Bayesian machinery can establish connections among models in computational dynamics, even when the data in use is noisy. The software used to generate the results reported herein is available in a public repository for unfettered use and distribution.
Auction-based Federated Learning (AFL) has attracted extensive research interest due to its ability to motivate data owners to join FL through economic means. Existing works assume that only one data consumer and multiple data owners exist in an AFL marketplace (i.e., a monopoly market). Therefore, data owners bid to join the data consumer for FL. However, this assumption is not realistic in practical AFL marketplaces in which multiple data consumers can compete to attract data owners to join their respective FL tasks. In this paper, we bridge this gap by proposing a first-of-its-kind utility-maximizing bidding strategy for data consumers in federated learning (Fed-Bidder). It enables multiple FL data consumers to compete for data owners via AFL effectively and efficiently by providing with utility estimation capabilities which can accommodate diverse forms of winning functions, each reflecting different market dynamics. Extensive experiments based on six commonly adopted benchmark datasets show that Fed-Bidder is significantly more advantageous compared to four state-of-the-art approaches.
Back-support exoskeletons are commonly used in the workplace to reduce low back pain risk for workers performing demanding activities. However, for the assistance of tasks differing from lifting, back-support exoskeletons potential has not been exploited extensively. This work focuses on the use of an active back-support exoskeleton to assist carrying. Two control strategies are designed that modulate the exoskeleton torques to comply with the task assistance requirements. In particular, two gait phase detection frameworks are exploited to adapt the assistance according to the legs' motion. The two strategies are assessed through an experimental analysis on ten subjects. Carrying task is performed without and with the exoskeleton assistance. Results prove the potential of the presented controls in assisting the task without hindering the gait movement and improving the usability experienced by users. Moreover, the exoskeleton assistance significantly reduces the lumbar load associated with the task, demonstrating its promising use for risk mitigation in the workplace.
We develop the first active learning method in the predict-then-optimize framework. Specifically, we develop a learning method that sequentially decides whether to request the "labels" of feature samples from an unlabeled data stream, where the labels correspond to the parameters of an optimization model for decision-making. Our active learning method is the first to be directly informed by the decision error induced by the predicted parameters, which is referred to as the Smart Predict-then-Optimize (SPO) loss. Motivated by the structure of the SPO loss, our algorithm adopts a margin-based criterion utilizing the concept of distance to degeneracy and minimizes a tractable surrogate of the SPO loss on the collected data. In particular, we develop an efficient active learning algorithm with both hard and soft rejection variants, each with theoretical excess risk (i.e., generalization) guarantees. We further derive bounds on the label complexity, which refers to the number of samples whose labels are acquired to achieve a desired small level of SPO risk. Under some natural low-noise conditions, we show that these bounds can be better than the naive supervised learning approach that labels all samples. Furthermore, when using the SPO+ loss function, a specialized surrogate of the SPO loss, we derive a significantly smaller label complexity under separability conditions. We also present numerical evidence showing the practical value of our proposed algorithms in the settings of personalized pricing and the shortest path problem.
A large variety of real-world Reinforcement Learning (RL) tasks is characterized by a complex and heterogeneous structure that makes end-to-end (or flat) approaches hardly applicable or even infeasible. Hierarchical Reinforcement Learning (HRL) provides general solutions to address these problems thanks to a convenient multi-level decomposition of the tasks, making their solution accessible. Although often used in practice, few works provide theoretical guarantees to justify this outcome effectively. Thus, it is not yet clear when to prefer such approaches compared to standard flat ones. In this work, we provide an option-dependent upper bound to the regret suffered by regret minimization algorithms in finite-horizon problems. We illustrate that the performance improvement derives from the planning horizon reduction induced by the temporal abstraction enforced by the hierarchical structure. Then, focusing on a sub-setting of HRL approaches, the options framework, we highlight how the average duration of the available options affects the planning horizon and, consequently, the regret itself. Finally, we relax the assumption of having pre-trained options to show how in particular situations, learning hierarchically from scratch could be preferable to using a standard approach.
The Importance Markov chain is a novel algorithm bridging the gap between rejection sampling and importance sampling, moving from one to the other through a tuning parameter. Based on a modified sample of an instrumental Markov chain targeting an instrumental distribution (typically via a MCMC kernel), the Importance Markov chain produces an extended Markov chain where the marginal distribution of the first component converges to the target distribution. For example, when targeting a multimodal distribution, the instrumental distribution can be chosen as a tempered version of the target which allows the algorithm to explore its modes more efficiently. We obtain a Law of Large Numbers and a Central Limit Theorem as well as geometric ergodicity for this extended kernel under mild assumptions on the instrumental kernel. Computationally, the algorithm is easy to implement and preexisting librairies can be used to sample from the instrumental distribution.
Intelligent vehicles (IVs) have gained worldwide attention due to their increased convenience, safety advantages, and potential commercial value. Despite predictions of commercial deployment by 2025, implementation remains limited to small-scale validation, with precise tracking controllers and motion planners being essential prerequisites for IVs. This paper reviews state-of-the-art motion planning methods for IVs, including pipeline planning and end-to-end planning methods. The study examines the selection, expansion, and optimization operations in a pipeline method, while it investigates training approaches and validation scenarios for driving tasks in end-to-end methods. Experimental platforms are reviewed to assist readers in choosing suitable training and validation strategies. A side-by-side comparison of the methods is provided to highlight their strengths and limitations, aiding system-level design choices. Current challenges and future perspectives are also discussed in this survey.
This paper aims to mitigate straggler effects in synchronous distributed learning for multi-agent reinforcement learning (MARL) problems. Stragglers arise frequently in a distributed learning system, due to the existence of various system disturbances such as slow-downs or failures of compute nodes and communication bottlenecks. To resolve this issue, we propose a coded distributed learning framework, which speeds up the training of MARL algorithms in the presence of stragglers, while maintaining the same accuracy as the centralized approach. As an illustration, a coded distributed version of the multi-agent deep deterministic policy gradient(MADDPG) algorithm is developed and evaluated. Different coding schemes, including maximum distance separable (MDS)code, random sparse code, replication-based code, and regular low density parity check (LDPC) code are also investigated. Simulations in several multi-robot problems demonstrate the promising performance of the proposed framework.
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