This paper studies safety guarantees for systems with time-varying control bounds. It has been shown that optimizing quadratic costs subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) using Control Barrier Functions (CBFs). One of the main challenges in this method is that the CBF-based QP could easily become infeasible under tight control bounds, especially when the control bounds are time-varying. The recently proposed adaptive CBFs have addressed such infeasibility issues, but require extensive and non-trivial hyperparameter tuning for the CBF-based QP and may introduce overshooting control near the boundaries of safe sets. To address these issues, we propose a new type of adaptive CBFs called Auxiliary Variable CBFs (AVCBFs). Specifically, we introduce an auxiliary variable that multiplies each CBF itself, and define dynamics for the auxiliary variable to adapt it in constructing the corresponding CBF constraint. In this way, we can improve the feasibility of the CBF-based QP while avoiding extensive parameter tuning with non-overshooting control since the formulation is identical to classical CBF methods. We demonstrate the advantages of using AVCBFs and compare them with existing techniques on an Adaptive Cruise Control (ACC) problem with time-varying control bounds.
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Modeling of real-world biological multi-agents is a fundamental problem in various scientific and engineering fields. Reinforcement learning (RL) is a powerful framework to generate flexible and diverse behaviors in cyberspace; however, when modeling real-world biological multi-agents, there is a domain gap between behaviors in the source (i.e., real-world data) and the target (i.e., cyberspace for RL), and the source environment parameters are usually unknown. In this paper, we propose a method for adaptive action supervision in RL from real-world demonstrations in multi-agent scenarios. We adopt an approach that combines RL and supervised learning by selecting actions of demonstrations in RL based on the minimum distance of dynamic time warping for utilizing the information of the unknown source dynamics. This approach can be easily applied to many existing neural network architectures and provide us with an RL model balanced between reproducibility as imitation and generalization ability to obtain rewards in cyberspace. In the experiments, using chase-and-escape and football tasks with the different dynamics between the unknown source and target environments, we show that our approach achieved a balance between the reproducibility and the generalization ability compared with the baselines. In particular, we used the tracking data of professional football players as expert demonstrations in football and show successful performances despite the larger gap between behaviors in the source and target environments than the chase-and-escape task.
Multi-agent systems can be extremely efficient when working concurrently and collaboratively, e.g., for transportation, maintenance, search and rescue. Coordination of such teams often involves two aspects: (i) selecting appropriate sub-teams for different tasks; (ii) designing collaborative control strategies to execute these tasks. The former aspect can be combinatorial w.r.t. the team size, while the latter requires optimization over joint state-spaces under geometric and dynamic constraints. Existing work often tackles one aspect by assuming the other is given, while ignoring their close dependency. This work formulates such problems as combinatorial-hybrid optimizations (CHO), where both the discrete modes of collaboration and the continuous control parameters are optimized simultaneously and iteratively. The proposed framework consists of two interleaved layers: the dynamic formation of task coalitions and the hybrid optimization of collaborative behaviors. Overall feasibility and costs of different coalitions performing various tasks are approximated at different granularities to improve the computational efficiency. At last, a Nash-stable strategy for both task assignment and execution is derived with provable guarantee on the feasibility and quality. Two non-trivial applications of collaborative transportation and dynamic capture are studied against several baselines.
We propose enhancing trajectory optimization methods through the incorporation of two key ideas: variable-grasp pose sampling and trajectory commitment. Our iterative approach samples multiple grasp poses, increasing the likelihood of finding a solution while gradually narrowing the optimization horizon towards the goal region for improved computational efficiency. We conduct experiments comparing our approach with sampling-based planning and fixed-goal optimization. In simulated experiments featuring 4 different task scenes, our approach consistently outperforms baselines by generating lower-cost trajectories and achieving higher success rates in challenging constrained and cluttered environments, at the trade-off of longer computation times. Real-world experiments further validate the superiority of our approach in generating lower-cost trajectories and exhibiting enhanced robustness. While we acknowledge the limitations of our experimental design, our proposed approach holds significant potential for enhancing trajectory optimization methods and offers a promising solution for achieving consistent and reliable robotic manipulation.
Post-market safety surveillance is an integral part of mass vaccination programs. Typically relying on sequential analysis of real-world health data as they accrue, safety surveillance is challenged by the difficulty of sequential multiple testing and by biases induced by residual confounding. The current standard approach based on the maximized sequential probability ratio test (MaxSPRT) fails to satisfactorily address these practical challenges and it remains a rigid framework that requires pre-specification of the surveillance schedule. We develop an alternative Bayesian surveillance procedure that addresses both challenges using a more flexible framework. We adopt a joint statistical modeling approach to sequentially estimate the effect of vaccine exposure on the adverse event of interest and correct for estimation bias by simultaneously analyzing a large set of negative control outcomes through a Bayesian hierarchical model. We then compute a posterior probability of the alternative hypothesis via Markov chain Monte Carlo sampling and use it for sequential detection of safety signals. Through an empirical evaluation using six US observational healthcare databases covering more than 360 million patients, we benchmark the proposed procedure against MaxSPRT on testing errors and estimation accuracy, under two epidemiological designs, the historical comparator and the self-controlled case series. We demonstrate that our procedure substantially reduces Type 1 error rates, maintains high statistical power, delivers fast signal detection, and provides considerably more accurate estimation. As an effort to promote open science, we present all empirical results in an R ShinyApp and provide full implementation of our method in the R package EvidenceSynthesis.
This paper presents a dataset containing recordings of the electroencephalogram (EEG) and the electromyogram (EMG) from eight subjects who were assisted in moving their right arm by an active orthosis device. The supported movements were elbow joint movements, i.e., flexion and extension of the right arm. While the orthosis was actively moving the subject's arm, some errors were deliberately introduced for a short duration of time. During this time, the orthosis moved in the opposite direction. In this paper, we explain the experimental setup and present some behavioral analyses across all subjects. Additionally, we present an average event-related potential analysis for one subject to offer insights into the data quality and the EEG activity caused by the error introduction. The dataset described herein is openly accessible. The aim of this study was to provide a dataset to the research community, particularly for the development of new methods in the asynchronous detection of erroneous events from the EEG. We are especially interested in the tactile and haptic-mediated recognition of errors, which has not yet been sufficiently investigated in the literature. We hope that the detailed description of the orthosis and the experiment will enable its reproduction and facilitate a systematic investigation of the influencing factors in the detection of erroneous behavior of assistive systems by a large community.
Off-policy evaluation (OPE) is the problem of estimating the value of a target policy using historical data collected under a different logging policy. OPE methods typically assume overlap between the target and logging policy, enabling solutions based on importance weighting and/or imputation. In this work, we approach OPE without assuming either overlap or a well-specified model by considering a strategy based on partial identification under non-parametric assumptions on the conditional mean function, focusing especially on Lipschitz smoothness. Under such smoothness assumptions, we formulate a pair of linear programs whose optimal values upper and lower bound the contributions of the no-overlap region to the off-policy value. We show that these linear programs have a concise closed form solution that can be computed efficiently and that their solutions converge, under the Lipschitz assumption, to the sharp partial identification bounds on the off-policy value. Furthermore, we show that the rate of convergence is minimax optimal, up to log factors. We deploy our methods on two semi-synthetic examples, and obtain informative and valid bounds that are tighter than those possible without smoothness assumptions.
Robots with the ability to balance time against the thoroughness of search have the potential to provide time-critical assistance in applications such as search and rescue. Current advances in ergodic coverage-based search methods have enabled robots to completely explore and search an area in a fixed amount of time. However, optimizing time against the quality of autonomous ergodic search has yet to be demonstrated. In this paper, we investigate solutions to the time-optimal ergodic search problem for fast and adaptive robotic search and exploration. We pose the problem as a minimum time problem with an ergodic inequality constraint whose upper bound regulates and balances the granularity of search against time. Solutions to the problem are presented analytically using Pontryagin's conditions of optimality and demonstrated numerically through a direct transcription optimization approach. We show the efficacy of the approach in generating time-optimal ergodic search trajectories in simulation and with drone experiments in a cluttered environment. Obstacle avoidance is shown to be readily integrated into our formulation, and we perform ablation studies that investigate parameter dependence on optimized time and trajectory sensitivity for search.
The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.
Neural networks have shown tremendous growth in recent years to solve numerous problems. Various types of neural networks have been introduced to deal with different types of problems. However, the main goal of any neural network is to transform the non-linearly separable input data into more linearly separable abstract features using a hierarchy of layers. These layers are combinations of linear and nonlinear functions. The most popular and common non-linearity layers are activation functions (AFs), such as Logistic Sigmoid, Tanh, ReLU, ELU, Swish and Mish. In this paper, a comprehensive overview and survey is presented for AFs in neural networks for deep learning. Different classes of AFs such as Logistic Sigmoid and Tanh based, ReLU based, ELU based, and Learning based are covered. Several characteristics of AFs such as output range, monotonicity, and smoothness are also pointed out. A performance comparison is also performed among 18 state-of-the-art AFs with different networks on different types of data. The insights of AFs are presented to benefit the researchers for doing further research and practitioners to select among different choices. The code used for experimental comparison is released at: \url{//github.com/shivram1987/ActivationFunctions}.
Bid optimization for online advertising from single advertiser's perspective has been thoroughly investigated in both academic research and industrial practice. However, existing work typically assume competitors do not change their bids, i.e., the wining price is fixed, leading to poor performance of the derived solution. Although a few studies use multi-agent reinforcement learning to set up a cooperative game, they still suffer the following drawbacks: (1) They fail to avoid collusion solutions where all the advertisers involved in an auction collude to bid an extremely low price on purpose. (2) Previous works cannot well handle the underlying complex bidding environment, leading to poor model convergence. This problem could be amplified when handling multiple objectives of advertisers which are practical demands but not considered by previous work. In this paper, we propose a novel multi-objective cooperative bid optimization formulation called Multi-Agent Cooperative bidding Games (MACG). MACG sets up a carefully designed multi-objective optimization framework where different objectives of advertisers are incorporated. A global objective to maximize the overall profit of all advertisements is added in order to encourage better cooperation and also to protect self-bidding advertisers. To avoid collusion, we also introduce an extra platform revenue constraint. We analyze the optimal functional form of the bidding formula theoretically and design a policy network accordingly to generate auction-level bids. Then we design an efficient multi-agent evolutionary strategy for model optimization. Offline experiments and online A/B tests conducted on the Taobao platform indicate both single advertiser's objective and global profit have been significantly improved compared to state-of-art methods.
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