S. Shankar Sastry

Anil Aswani, Humberto Gonzalez, S. Shankar Sastry et al.

Controller design faces a trade-off between robustness and performance, and the reliability of linear controllers has caused many practitioners to focus on the former. However, there is renewed interest in improving system performance to deal with growing energy constraints. This paper describes a learning-based model predictive control (LBMPC) scheme that provides deterministic guarantees on robustness, while statistical identification tools are used to identify richer models of the system in order to improve performance; the benefits of this framework are that it handles state and input constraints, optimizes system performance with respect to a cost function, and can be designed to use a wide variety of parametric or nonparametric statistical tools. The main insight of LBMPC is that safety and performance can be decoupled under reasonable conditions in an optimization framework by maintaining two models of the system. The first is an approximate model with bounds on its uncertainty, and the second model is updated by statistical methods. LBMPC improves performance by choosing inputs that minimize a cost subject to the learned dynamics, and it ensures safety and robustness by checking whether these same inputs keep the approximate model stable when it is subject to uncertainty. Furthermore, we show that if the system is sufficiently excited, then the LBMPC control action probabilistically converges to that of an MPC computed using the true dynamics.

Allen Y. Yang, Zihan Zhou, Arvind Ganesh et al.

L1-minimization refers to finding the minimum L1-norm solution to an underdetermined linear system b=Ax. Under certain conditions as described in compressive sensing theory, the minimum L1-norm solution is also the sparsest solution. In this paper, our study addresses the speed and scalability of its algorithms. In particular, we focus on the numerical implementation of a sparsity-based classification framework in robust face recognition, where sparse representation is sought to recover human identities from very high-dimensional facial images that may be corrupted by illumination, facial disguise, and pose variation. Although the underlying numerical problem is a linear program, traditional algorithms are known to suffer poor scalability for large-scale applications. We investigate a new solution based on a classical convex optimization framework, known as Augmented Lagrangian Methods (ALM). The new convex solvers provide a viable solution to real-world, time-critical applications such as face recognition. We conduct extensive experiments to validate and compare the performance of the ALM algorithms against several popular L1-minimization solvers, including interior-point method, Homotopy, FISTA, SESOP-PCD, approximate message passing (AMP) and TFOCS. To aid peer evaluation, the code for all the algorithms has been made publicly available.

Henrik Ohlsson, Lillian Ratliff, Roy Dong et al.

Blind system identification is known to be a hard ill-posed problem and without further assumptions, no unique solution is at hand. In this contribution, we are concerned with the task of identifying an ARX model from only output measurements. Driven by the task of identifying systems that are turned on and off at unknown times, we seek a piecewise constant input and a corresponding ARX model which approximates the measured outputs. We phrase this as a rank minimization problem and present a relaxed convex formulation to approximate its solution. The proposed method was developed to model power consumption of electrical appliances and is now a part of a bigger energy disaggregation framework. Code will be made available online.

Maria G. Mendoza, Pan-Yang Su, Bryce L. Ferguson et al.

We study dynamic multi-robot task allocation under uncertain task completion, time-window constraints, and incomplete information. Tasks arrive online over a finite horizon and must be completed within specified deadlines, while agents operate from distributed hubs with limited sensing and communication. We model incomplete information through hub-based sensing regions that determine task visibility and a communication graph that governs inter-hub information exchange. Using this framework, we propose Iterative Best Response (IBR), a decentralized policy in which each agent selects the task that maximizes its marginal contribution to the locally observed welfare. We compare IBR against three baselines: Earliest Due Date first (EDD), Hungarian algorithm, and Stochastic Conflict-Based Allocation (SCoBA), on a city-scale package-delivery domain with up to 100 drones and varying task arrival scenarios. Under full and sparse communication, IBR achieves competitive task-completion performance with lower computation time.

Zixuan Chen, Xialin He, Yen-Jen Wang et al.

Reinforcement learning combined with sim-to-real transfer offers a general framework for developing locomotion controllers for legged robots. To facilitate successful deployment in the real world, smoothing techniques, such as low-pass filters and smoothness rewards, are often employed to develop policies with smooth behaviors. However, because these techniques are non-differentiable and usually require tedious tuning of a large set of hyperparameters, they tend to require extensive manual tuning for each robotic platform. To address this challenge and establish a general technique for enforcing smooth behaviors, we propose a simple and effective method that imposes a Lipschitz constraint on a learned policy, which we refer to as Lipschitz-Constrained Policies (LCP). We show that the Lipschitz constraint can be implemented in the form of a gradient penalty, which provides a differentiable objective that can be easily incorporated with automatic differentiation frameworks. We demonstrate that LCP effectively replaces the need for smoothing rewards or low-pass filters and can be easily integrated into training frameworks for many distinct humanoid robots. We extensively evaluate LCP in both simulation and real-world humanoid robots, producing smooth and robust locomotion controllers. All simulation and deployment code, along with complete checkpoints, is available on our project page: https://lipschitz-constrained-policy.github.io.

Jaewon Jeong, Pan-Yang Su, S. Shankar Sastry et al.

Many incentive design problems must contend with information asymmetries due to non-observation of efficiency (adverse selection) or non-observation of effort (moral hazard). And although a growing body of literature considers incentive design in control systems, the problem of designing incentives for control systems under information asymmetries has been less well-studied. This paper considers a model of moral hazard within control systems. In our model, the control system is described by an (affine) linear time-invariant (LTI) system with process noise. There is an agent who gets to choose (from between two choices) a linear state-feedback controller to apply to the LTI system, with one of the state-feedback controllers having a higher quadratic cost on the control inputs than the other. Our goal is to design a payment scheme that incentivizes the agent to choose the state-feedback controller that minimizes a quadratic cost on system states plus the time-discounted payment amount, subject to the understanding that the agent bears the control cost while being risk-averse with respect to their time-discounted payment. We formulate the problem as a constrained optimization, and prove that for a payment given after a fixed (but optimizable) time horizon the optimal payment scheme chooses the payment amount using a likelihood ratio hypothesis test. We numerically demonstrate our results by applying the derived optimal payment scheme to two examples: load frequency control (LFC) in power systems and wellness interventions for body weight loss.

Tijana Zrnic, Eric Mazumdar, S. Shankar Sastry et al.

As predictive models are deployed into the real world, they must increasingly contend with strategic behavior. A growing body of work on strategic classification treats this problem as a Stackelberg game: the decision-maker "leads" in the game by deploying a model, and the strategic agents "follow" by playing their best response to the deployed model. Importantly, in this framing, the burden of learning is placed solely on the decision-maker, while the agents' best responses are implicitly treated as instantaneous. In this work, we argue that the order of play in strategic classification is fundamentally determined by the relative frequencies at which the decision-maker and the agents adapt to each other's actions. In particular, by generalizing the standard model to allow both players to learn over time, we show that a decision-maker that makes updates faster than the agents can reverse the order of play, meaning that the agents lead and the decision-maker follows. We observe in standard learning settings that such a role reversal can be desirable for both the decision-maker and the strategic agents. Finally, we show that a decision-maker with the freedom to choose their update frequency can induce learning dynamics that converge to Stackelberg equilibria with either order of play.

Chinmay Maheshwari, Chih-Yuan Chiu, Eric Mazumdar et al.

Min-max optimization is emerging as a key framework for analyzing problems of robustness to strategically and adversarially generated data. We propose a random reshuffling-based gradient free Optimistic Gradient Descent-Ascent algorithm for solving convex-concave min-max problems with finite sum structure. We prove that the algorithm enjoys the same convergence rate as that of zeroth-order algorithms for convex minimization problems. We further specialize the algorithm to solve distributionally robust, decision-dependent learning problems, where gradient information is not readily available. Through illustrative simulations, we observe that our proposed approach learns models that are simultaneously robust against adversarial distribution shifts and strategic decisions from the data sources, and outperforms existing methods from the strategic classification literature.

Tyler Westenbroek, Max Simchowitz, Michael I. Jordan et al.

%!TEX root = LCSS_main_max.tex The widespread adoption of nonlinear Receding Horizon Control (RHC) strategies by industry has led to more than 30 years of intense research efforts to provide stability guarantees for these methods. However, current theoretical guarantees require that each (generally nonconvex) planning problem can be solved to (approximate) global optimality, which is an unrealistic requirement for the derivative-based local optimization methods generally used in practical implementations of RHC. This paper takes the first step towards understanding stability guarantees for nonlinear RHC when the inner planning problem is solved to first-order stationary points, but not necessarily global optima. Special attention is given to feedback linearizable systems, and a mixture of positive and negative results are provided. We establish that, under certain strong conditions, first-order solutions to RHC exponentially stabilize linearizable systems. Surprisingly, these conditions can hold even in situations where there may be \textit{spurious local minima.} Crucially, this guarantee requires that state costs applied to the planning problems are in a certain sense `compatible' with the global geometry of the system, and a simple counter-example demonstrates the necessity of this condition. These results highlight the need to rethink the role of global geometry in the context of optimization-based control.

David L. McPherson, Kaylene C. Stocking, S. Shankar Sastry

When an expert operates a perilous dynamic system, ideal constraint information is tacitly contained in their demonstrated trajectories and controls. The likelihood of these demonstrations can be computed, given the system dynamics and task objective, and the maximum likelihood constraints can be identified. Prior constraint inference work has focused mainly on deterministic models. Stochastic models, however, can capture the uncertainty and risk tolerance that are often present in real systems of interest. This paper extends maximum likelihood constraint inference to stochastic applications by using maximum causal entropy likelihoods. Furthermore, we propose an efficient algorithm that computes constraint likelihood and risk tolerance in a unified Bellman backup, allowing us to generalize to stochastic systems without increasing computational complexity.

Vicenc Rubies-Royo, Eric Mazumdar, Roy Dong et al.

In this work we present a multi-armed bandit framework for online expert selection in Markov decision processes and demonstrate its use in high-dimensional settings. Our method takes a set of candidate expert policies and switches between them to rapidly identify the best performing expert using a variant of the classical upper confidence bound algorithm, thus ensuring low regret in the overall performance of the system. This is useful in applications where several expert policies may be available, and one needs to be selected at run-time for the underlying environment.

Oladapo Afolabi, Allen Y. Yang, S. Shankar Sastry

Recent advances in computer graphics and computer vision have found successful application of deep neural network models for 3D shapes based on signed distance functions (SDFs) that are useful for shape representation, retrieval, and completion. However, this approach has been limited by the need to have query shapes in the same canonical scale and pose as those observed during training, restricting its effectiveness on real world scenes. We present a formulation to overcome this issue by jointly estimating shape and similarity transform parameters. We conduct experiments to demonstrate the effectiveness of this formulation on synthetic and real datasets and report favorable comparisons to the state of the art. Finally, we also emphasize the viability of this approach as a form of 3D model compression.

Fernando Castañeda, Mathias Wulfman, Ayush Agrawal et al.

The main drawbacks of input-output linearizing controllers are the need for precise dynamics models and not being able to account for input constraints. Model uncertainty is common in almost every robotic application and input saturation is present in every real world system. In this paper, we address both challenges for the specific case of bipedal robot control by the use of reinforcement learning techniques. Taking the structure of a standard input-output linearizing controller, we use an additive learned term that compensates for model uncertainty. Moreover, by adding constraints to the learning problem we manage to boost the performance of the final controller when input limits are present. We demonstrate the effectiveness of the designed framework for different levels of uncertainty on the five-link planar walking robot RABBIT.

Tyler Westenbroek, Eric Mazumdar, David Fridovich-Keil et al.

This paper proposes a framework for adaptively learning a feedback linearization-based tracking controller for an unknown system using discrete-time model-free policy-gradient parameter update rules. The primary advantage of the scheme over standard model-reference adaptive control techniques is that it does not require the learned inverse model to be invertible at all instances of time. This enables the use of general function approximators to approximate the linearizing controller for the system without having to worry about singularities. However, the discrete-time and stochastic nature of these algorithms precludes the direct application of standard machinery from the adaptive control literature to provide deterministic stability proofs for the system. Nevertheless, we leverage these techniques alongside tools from the stochastic approximation literature to demonstrate that with high probability the tracking and parameter errors concentrate near zero when a certain persistence of excitation condition is satisfied. A simulated example of a double pendulum demonstrates the utility of the proposed theory. 1

Valmik Prabhu, Amay Saxena, S. Shankar Sastry

We present a novel first order controller for systems evolving on matrix Lie groups, a major use case of which is Cartesian velocity control on robot manipulators. This controller achieves global exponential trajectory tracking on a number of commonly used Lie groups including the Special Orthogonal Group SO(n), the Special Euclidean Group SE(n), and the General Linear Group over complex numbers GL(n, C). Additionally, this controller achieves local exponential trajectory tracking on all matrix Lie groups. We demonstrate the effectiveness of this controller in simulation on a number of different Lie groups as well as on hardware with a 7-DOF Sawyer robot arm.

Andreea Bobu, Dexter R. R. Scobee, Jaime F. Fisac et al.

Robots need models of human behavior for both inferring human goals and preferences, and predicting what people will do. A common model is the Boltzmann noisily-rational decision model, which assumes people approximately optimize a reward function and choose trajectories in proportion to their exponentiated reward. While this model has been successful in a variety of robotics domains, its roots lie in econometrics, and in modeling decisions among different discrete options, each with its own utility or reward. In contrast, human trajectories lie in a continuous space, with continuous-valued features that influence the reward function. We propose that it is time to rethink the Boltzmann model, and design it from the ground up to operate over such trajectory spaces. We introduce a model that explicitly accounts for distances between trajectories, rather than only their rewards. Rather than each trajectory affecting the decision independently, similar trajectories now affect the decision together. We start by showing that our model better explains human behavior in a user study. We then analyze the implications this has for robot inference, first in toy environments where we have ground truth and find more accurate inference, and finally for a 7DOF robot arm learning from user demonstrations.

Kamil Nar, S. Shankar Sastry

When an online learning algorithm is used to estimate the unknown parameters of a model, the signals interacting with the parameter estimates should not decay too quickly for the optimal values to be discovered correctly. This requirement is referred to as persistency of excitation, and it arises in various contexts, such as optimization with stochastic gradient methods, exploration for multi-armed bandits, and adaptive control of dynamical systems. While training a neural network, the iterative optimization algorithm involved also creates an online learning problem, and consequently, correct estimation of the optimal parameters requires persistent excitation of the network weights. In this work, we analyze the dynamics of the gradient descent algorithm while training a two-layer neural network with two different loss functions, the squared-error loss and the cross-entropy loss; and we obtain conditions to guarantee persistent excitation of the network weights. We then show that these conditions are difficult to satisfy when a multi-layer network is trained for a classification task, for the signals in the intermediate layers of the network become low-dimensional during training and fail to remain persistently exciting. To provide a remedy, we delve into the classical regularization terms used for linear models, reinterpret them as a means to ensure persistent excitation of the model parameters, and propose an algorithm for neural networks by building an analogy. The results in this work shed some light on why adversarial examples have become a challenging problem for neural networks, why merely augmenting training data sets will not be an effective approach to address them, and why there may not exist a data-independent regularization term for neural networks, which involve only the model parameters but not the training data.

Tyler Westenbroek, David Fridovich-Keil, Eric Mazumdar et al.

We present a novel approach to control design for nonlinear systems which leverages model-free policy optimization techniques to learn a linearizing controller for a physical plant with unknown dynamics. Feedback linearization is a technique from nonlinear control which renders the input-output dynamics of a nonlinear plant \emph{linear} under application of an appropriate feedback controller. Once a linearizing controller has been constructed, desired output trajectories for the nonlinear plant can be tracked using a variety of linear control techniques. However, the calculation of a linearizing controller requires a precise dynamics model for the system. As a result, model-based approaches for learning exact linearizing controllers generally require a simple, highly structured model of the system with easily identifiable parameters. In contrast, the model-free approach presented in this paper is able to approximate the linearizing controller for the plant using general function approximation architectures. Specifically, we formulate a continuous-time optimization problem over the parameters of a learned linearizing controller whose optima are the set of parameters which best linearize the plant. We derive conditions under which the learning problem is (strongly) convex and provide guarantees which ensure the true linearizing controller for the plant is recovered. We then discuss how model-free policy optimization algorithms can be used to solve a discrete-time approximation to the problem using data collected from the real-world plant. The utility of the framework is demonstrated in simulation and on a real-world robotic platform.

Dexter R. R. Scobee, S. Shankar Sastry

While most approaches to the problem of Inverse Reinforcement Learning (IRL) focus on estimating a reward function that best explains an expert agent's policy or demonstrated behavior on a control task, it is often the case that such behavior is more succinctly represented by a simple reward combined with a set of hard constraints. In this setting, the agent is attempting to maximize cumulative rewards subject to these given constraints on their behavior. We reformulate the problem of IRL on Markov Decision Processes (MDPs) such that, given a nominal model of the environment and a nominal reward function, we seek to estimate state, action, and feature constraints in the environment that motivate an agent's behavior. Our approach is based on the Maximum Entropy IRL framework, which allows us to reason about the likelihood of an expert agent's demonstrations given our knowledge of an MDP. Using our method, we can infer which constraints can be added to the MDP to most increase the likelihood of observing these demonstrations. We present an algorithm which iteratively infers the Maximum Likelihood Constraint to best explain observed behavior, and we evaluate its efficacy using both simulated behavior and recorded data of humans navigating around an obstacle.

Eric Mazumdar, Lillian J. Ratliff, Michael I. Jordan et al.

We show by counterexample that policy-gradient algorithms have no guarantees of even local convergence to Nash equilibria in continuous action and state space multi-agent settings. To do so, we analyze gradient-play in N-player general-sum linear quadratic games, a classic game setting which is recently emerging as a benchmark in the field of multi-agent learning. In such games the state and action spaces are continuous and global Nash equilibria can be found be solving coupled Ricatti equations. Further, gradient-play in LQ games is equivalent to multi agent policy-gradient. We first show that these games are surprisingly not convex games. Despite this, we are still able to show that the only critical points of the gradient dynamics are global Nash equilibria. We then give sufficient conditions under which policy-gradient will avoid the Nash equilibria, and generate a large number of general-sum linear quadratic games that satisfy these conditions. In such games we empirically observe the players converging to limit cycles for which the time average does not coincide with a Nash equilibrium. The existence of such games indicates that one of the most popular approaches to solving reinforcement learning problems in the classic reinforcement learning setting has no local guarantee of convergence in multi-agent settings. Further, the ease with which we can generate these counterexamples suggests that such situations are not mere edge cases and are in fact quite common.

Tyler Westenbroek, Roy Dong, Lillian J. Ratliff et al.

In recent years, data has played an increasingly important role in the economy as a good in its own right. In many settings, data aggregators cannot directly verify the quality of the data they purchase, nor the effort exerted by data sources when creating the data. Recent work has explored mechanisms to ensure that the data sources share high quality data with a single data aggregator, addressing the issue of moral hazard. Oftentimes, there is a unique, socially efficient solution. In this paper, we consider data markets where there is more than one data aggregator. Since data can be cheaply reproduced and transmitted once created, data sources may share the same data with more than one aggregator, leading to free-riding between data aggregators. This coupling can lead to non-uniqueness of equilibria and social inefficiency. We examine a particular class of mechanisms that have received study recently in the literature, and we characterize all the generalized Nash equilibria of the resulting data market. We show that, in contrast to the single-aggregator case, there is either infinitely many generalized Nash equilibria or none. We also provide necessary and sufficient conditions for all equilibria to be socially inefficient. In our analysis, we identify the components of these mechanisms which give rise to these undesirable outcomes, showing the need for research into mechanisms for competitive settings with multiple data purchasers and sellers.

Kamil Nar, Orhan Ocal, S. Shankar Sastry et al.

State-of-the-art neural networks are vulnerable to adversarial examples; they can easily misclassify inputs that are imperceptibly different than their training and test data. In this work, we establish that the use of cross-entropy loss function and the low-rank features of the training data have responsibility for the existence of these inputs. Based on this observation, we suggest that addressing adversarial examples requires rethinking the use of cross-entropy loss function and looking for an alternative that is more suited for minimization with low-rank features. In this direction, we present a training scheme called differential training, which uses a loss function defined on the differences between the features of points from opposite classes. We show that differential training can ensure a large margin between the decision boundary of the neural network and the points in the training dataset. This larger margin increases the amount of perturbation needed to flip the prediction of the classifier and makes it harder to find an adversarial example with small perturbations. We test differential training on a binary classification task with CIFAR-10 dataset and demonstrate that it radically reduces the ratio of images for which an adversarial example could be found -- not only in the training dataset, but in the test dataset as well.

Eric V. Mazumdar, Michael I. Jordan, S. Shankar Sastry

We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due to the existence of non-Nash stationary points. By taking advantage of the differential structure of the game, we construct an algorithm for which the local Nash equilibria are the only attracting fixed points. We also show that the algorithm exhibits no oscillatory behaviors in neighborhoods of equilibria and show that it has the same per-iteration complexity as other recently proposed algorithms. We conclude by validating the algorithm on two numerical examples: a toy example with multiple Nash equilibria and a non-Nash equilibrium, and the training of a small generative adversarial network (GAN).

Jaime F. Fisac, Eli Bronstein, Elis Stefansson et al.

The actions of an autonomous vehicle on the road affect and are affected by those of other drivers, whether overtaking, negotiating a merge, or avoiding an accident. This mutual dependence, best captured by dynamic game theory, creates a strong coupling between the vehicle's planning and its predictions of other drivers' behavior, and constitutes an open problem with direct implications on the safety and viability of autonomous driving technology. Unfortunately, dynamic games are too computationally demanding to meet the real-time constraints of autonomous driving in its continuous state and action space. In this paper, we introduce a novel game-theoretic trajectory planning algorithm for autonomous driving, that enables real-time performance by hierarchically decomposing the underlying dynamic game into a long-horizon "strategic" game with simplified dynamics and full information structure, and a short-horizon "tactical" game with full dynamics and a simplified information structure. The value of the strategic game is used to guide the tactical planning, implicitly extending the planning horizon, pushing the local trajectory optimization closer to global solutions, and, most importantly, quantitatively accounting for the autonomous vehicle and the human driver's ability and incentives to influence each other. In addition, our approach admits non-deterministic models of human decision-making, rather than relying on perfectly rational predictions. Our results showcase richer, safer, and more effective autonomous behavior in comparison to existing techniques.

Kamil Nar, S. Shankar Sastry

Training a neural network with the gradient descent algorithm gives rise to a discrete-time nonlinear dynamical system. Consequently, behaviors that are typically observed in these systems emerge during training, such as convergence to an orbit but not to a fixed point or dependence of convergence on the initialization. Step size of the algorithm plays a critical role in these behaviors: it determines the subset of the local optima that the algorithm can converge to, and it specifies the magnitude of the oscillations if the algorithm converges to an orbit. To elucidate the effects of the step size on training of neural networks, we study the gradient descent algorithm as a discrete-time dynamical system, and by analyzing the Lyapunov stability of different solutions, we show the relationship between the step size of the algorithm and the solutions that can be obtained with this algorithm. The results provide an explanation for several phenomena observed in practice, including the deterioration in the training error with increased depth, the hardness of estimating linear mappings with large singular values, and the distinct performance of deep residual networks.

David L. McPherson, Dexter R. R. Scobee, Joseph Menke et al.

When a human supervisor collaborates with a team of robots, their attention is divided and cognitive resources are at a premium. We aim to optimize the distribution of these resources and the flow of attention. To this end, we propose the model of an idealized supervisor to describe human behavior. Such a supervisor employs a potentially inaccurate internal model of the the robots' dynamics to judge safety. We represent these safety judgements by constructing a safe set from this internal model using reachability theory. When a robot leaves this safe set, the idealized supervisor will intervene to assist, regardless of whether or not the robot remains objectively safe. False positives, where a human supervisor incorrectly judges a robot to be in danger, needlessly consume supervisor attention. In this work, we propose a method that decreases false positives by learning the supervisor's safe set and using that information to govern robot behavior. We prove that robots behaving according to our approach will reduce the occurrence of false positives for our idealized supervisor model. Furthermore, we empirically validate our approach with a user study that demonstrates a significant ($p = 0.0328$) reduction in false positives for our method compared to a baseline safety controller.

Eric Mazumdar, Lillian J. Ratliff, S. Shankar Sastry

We formulate a general framework for competitive gradient-based learning that encompasses a wide breadth of multi-agent learning algorithms, and analyze the limiting behavior of competitive gradient-based learning algorithms using dynamical systems theory. For both general-sum and potential games, we characterize a non-negligible subset of the local Nash equilibria that will be avoided if each agent employs a gradient-based learning algorithm. We also shed light on the issue of convergence to non-Nash strategies in general- and zero-sum games, which may have no relevance to the underlying game, and arise solely due to the choice of algorithm. The existence and frequency of such strategies may explain some of the difficulties encountered when using gradient descent in zero-sum games as, e.g., in the training of generative adversarial networks. To reinforce the theoretical contributions, we provide empirical results that highlight the frequency of linear quadratic dynamic games (a benchmark for multi-agent reinforcement learning) that admit global Nash equilibria that are almost surely avoided by policy gradient.

Jaime F. Fisac, Chang Liu, Jessica B. Hamrick et al.

Collaboration requires coordination, and we coordinate by anticipating our teammates' future actions and adapting to their plan. In some cases, our teammates' actions early on can give us a clear idea of what the remainder of their plan is, i.e. what action sequence we should expect. In others, they might leave us less confident, or even lead us to the wrong conclusion. Our goal is for robot actions to fall in the first category: we want to enable robots to select their actions in such a way that human collaborators can easily use them to correctly anticipate what will follow. While previous work has focused on finding initial plans that convey a set goal, here we focus on finding two portions of a plan such that the initial portion conveys the final one. We introduce $t$-\ACty{}: a measure that quantifies the accuracy and confidence with which human observers can predict the remaining robot plan from the overall task goal and the observed initial $t$ actions in the plan. We contribute a method for generating $t$-predictable plans: we search for a full plan that accomplishes the task, but in which the first $t$ actions make it as easy as possible to infer the remaining ones. The result is often different from the most efficient plan, in which the initial actions might leave a lot of ambiguity as to how the task will be completed. Through an online experiment and an in-person user study with physical robots, we find that our approach outperforms a traditional efficiency-based planner in objective and subjective collaboration metrics.

Chang Liu, Jessica B. Hamrick, Jaime F. Fisac et al.

The study of human-robot interaction is fundamental to the design and use of robotics in real-world applications. Robots will need to predict and adapt to the actions of human collaborators in order to achieve good performance and improve safety and end-user adoption. This paper evaluates a human-robot collaboration scheme that combines the task allocation and motion levels of reasoning: the robotic agent uses Bayesian inference to predict the next goal of its human partner from his or her ongoing motion, and re-plans its own actions in real time. This anticipative adaptation is desirable in many practical scenarios, where humans are unable or unwilling to take on the cognitive overhead required to explicitly communicate their intent to the robot. A behavioral experiment indicates that the combination of goal inference and dynamic task planning significantly improves both objective and perceived performance of the human-robot team. Participants were highly sensitive to the differences between robot behaviors, preferring to work with a robot that adapted to their actions over one that did not.

Oladapo Afolabi, Katherine Driggs-Campbell, Roy Dong et al.

Despite growing attention in autonomy, there are still many open problems, including how autonomous vehicles will interact and communicate with other agents, such as human drivers and pedestrians. Unlike most approaches that focus on pedestrian detection and planning for collision avoidance, this paper considers modeling the interaction between human drivers and pedestrians and how it might influence map estimation, as a proxy for detection. We take a mapping inspired approach and incorporate people as sensors into mapping frameworks. By taking advantage of other agents' actions, we demonstrate how we can impute portions of the map that would otherwise be occluded. We evaluate our framework in human driving experiments and on real-world data, using occupancy grids and landmark-based mapping approaches. Our approach significantly improves overall environment awareness and out-performs standard mapping techniques.

Jaime F. Fisac, Monica A. Gates, Jessica B. Hamrick et al.

As intelligent systems gain autonomy and capability, it becomes vital to ensure that their objectives match those of their human users; this is known as the value-alignment problem. In robotics, value alignment is key to the design of collaborative robots that can integrate into human workflows, successfully inferring and adapting to their users' objectives as they go. We argue that a meaningful solution to value alignment must combine multi-agent decision theory with rich mathematical models of human cognition, enabling robots to tap into people's natural collaborative capabilities. We present a solution to the cooperative inverse reinforcement learning (CIRL) dynamic game based on well-established cognitive models of decision making and theory of mind. The solution captures a key reciprocity relation: the human will not plan her actions in isolation, but rather reason pedagogically about how the robot might learn from them; the robot, in turn, can anticipate this and interpret the human's actions pragmatically. To our knowledge, this work constitutes the first formal analysis of value alignment grounded in empirically validated cognitive models.

Ruoxi Jia, Roy Dong, S. Shankar Sastry et al.

Large-scale sensing and actuation infrastructures have allowed buildings to achieve significant energy savings; at the same time, these technologies introduce significant privacy risks that must be addressed. In this paper, we present a framework for modeling the trade-off between improved control performance and increased privacy risks due to occupancy sensing. More specifically, we consider occupancy-based HVAC control as the control objective and the location traces of individual occupants as the private variables. Previous studies have shown that individual location information can be inferred from occupancy measurements. To ensure privacy, we design an architecture that distorts the occupancy data in order to hide individual occupant location information while maintaining HVAC performance. Using mutual information between the individual's location trace and the reported occupancy measurement as a privacy metric, we are able to optimally design a scheme to minimize privacy risk subject to a control performance guarantee. We evaluate our framework using real-world occupancy data: first, we verify that our privacy metric accurately assesses the adversary's ability to infer private variables from the distorted sensor measurements; then, we show that control performance is maintained through simulations of building operations using these distorted occupancy readings.

Sanjit A. Seshia, Dorsa Sadigh, S. Shankar Sastry

Verified artificial intelligence (AI) is the goal of designing AI-based systems that that have strong, ideally provable, assurances of correctness with respect to mathematically-specified requirements. This paper considers Verified AI from a formal methods perspective. We describe five challenges for achieving Verified AI, and five corresponding principles for addressing these challenges.

Roy Dong, Walid Krichene, Alexandre M. Bayen et al.

As our ground transportation infrastructure modernizes, the large amount of data being measured, transmitted, and stored motivates an analysis of the privacy aspect of these emerging cyber-physical technologies. In this paper, we consider privacy in the routing game, where the origins and destinations of drivers are considered private. This is motivated by the fact that this spatiotemporal information can easily be used as the basis for inferences for a person's activities. More specifically, we consider the differential privacy of the mapping from the amount of flow for each origin-destination pair to the traffic flow measurements on each link of a traffic network. We use a stochastic online learning framework for the population dynamics, which is known to converge to the Nash equilibrium of the routing game. We analyze the sensitivity of this process and provide theoretical guarantees on the convergence rates as well as differential privacy values for these models. We confirm these with simulations on a small example.

Jan O. Biermeyer, Todd R. Templeton, Christian Berger et al.

After the three DARPA Grand Challenge contests many groups around the world have continued to actively research and work toward an autonomous vehicle capable of accomplishing a mission in a given context (e.g. desert, city) while following a set of prescribed rules, but none has been completely successful in uncontrolled environments, a task that many people trivially fulfill every day. We believe that, together with improving the sensors used in cars and the artificial intelligence algorithms used to process the information, the community should focus on the systems engineering aspects of the problem, i.e. the limitations of the car (in terms of space, power, or heat dissipation) and the limitations of the software development cycle. This paper explores these issues and our experiences overcoming them.

Ehsan Elhamifar, Guillermo Sapiro, S. Shankar Sastry

Finding an informative subset of a large collection of data points or models is at the center of many problems in computer vision, recommender systems, bio/health informatics as well as image and natural language processing. Given pairwise dissimilarities between the elements of a `source set' and a `target set,' we consider the problem of finding a subset of the source set, called representatives or exemplars, that can efficiently describe the target set. We formulate the problem as a row-sparsity regularized trace minimization problem. Since the proposed formulation is, in general, NP-hard, we consider a convex relaxation. The solution of our optimization finds representatives and the assignment of each element of the target set to each representative, hence, obtaining a clustering. We analyze the solution of our proposed optimization as a function of the regularization parameter. We show that when the two sets jointly partition into multiple groups, our algorithm finds representatives from all groups and reveals clustering of the sets. In addition, we show that the proposed framework can effectively deal with outliers. Our algorithm works with arbitrary dissimilarities, which can be asymmetric or violate the triangle inequality. To efficiently implement our algorithm, we consider an Alternating Direction Method of Multipliers (ADMM) framework, which results in quadratic complexity in the problem size. We show that the ADMM implementation allows to parallelize the algorithm, hence further reducing the computational time. Finally, by experiments on real-world datasets, we show that our proposed algorithm improves the state of the art on the two problems of scene categorization using representative images and time-series modeling and segmentation using representative~models.

Roy Dong, Alvaro A. Cárdenas, Lillian J. Ratliff et al.

The modernization of the electrical grid and the installation of smart meters come with many advantages to control and monitoring. However, in the wrong hands, the data might pose a privacy threat. In this paper, we consider the tradeoff between smart grid operations and the privacy of consumers. We analyze the tradeoff between smart grid operations and how often data is collected by considering a realistic direct-load control example using thermostatically controlled loads, and we give simulation results to show how its performance degrades as the sampling frequency decreases. Additionally, we introduce a new privacy metric, which we call inferential privacy. This privacy metric assumes a strong adversary model, and provides an upper bound on the adversary's ability to infer a private parameter, independent of the algorithm he uses. Combining these two results allow us to directly consider the tradeoff between better load control and consumer privacy.

Liansheng Zhuang, Tsung-Han Chan, Allen Y. Yang et al.

Single-sample face recognition is one of the most challenging problems in face recognition. We propose a novel algorithm to address this problem based on a sparse representation based classification (SRC) framework. The new algorithm is robust to image misalignment and pixel corruption, and is able to reduce required gallery images to one sample per class. To compensate for the missing illumination information traditionally provided by multiple gallery images, a sparse illumination learning and transfer (SILT) technique is introduced. The illumination in SILT is learned by fitting illumination examples of auxiliary face images from one or more additional subjects with a sparsely-used illumination dictionary. By enforcing a sparse representation of the query image in the illumination dictionary, the SILT can effectively recover and transfer the illumination and pose information from the alignment stage to the recognition stage. Our extensive experiments have demonstrated that the new algorithms significantly outperform the state of the art in the single-sample regime and with less restrictions. In particular, the single-sample face alignment accuracy is comparable to that of the well-known Deformable SRC algorithm using multiple gallery images per class. Furthermore, the face recognition accuracy exceeds those of the SRC and Extended SRC algorithms using hand labeled alignment initialization.

Katherine Driggs-Campbell, Guillaume Bellegarda, Victor Shia et al.

This report describes a new experimental setup for human-in-the-loop simulations. A force feedback simulator with four axis motion has been setup for real-time driving experiments. The simulator will move to simulate the forces a driver feels while driving, which allows for a realistic experience for the driver. This setup allows for flexibility and control for the researcher in a realistic simulation environment. Experiments concerning driver distraction can also be carried out safely in this test bed, in addition to multi-agent experiments. All necessary code to run the simulator, the additional sensors, and the basic processing is available for use.

Dorsa Sadigh, Henrik Ohlsson, S. Shankar Sastry et al.

Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework to handle outliers. The proposed framework takes the form of a convex optimization problem with an objective that trades off fit, rank and sparsity. As in robust PCA, it can be problematic to find a suitable regularization parameter. We show how the space in which a suitable parameter should be sought can be limited to a bounded open set of the two dimensional parameter space. In practice, this is very useful since it restricts the parameter space that is needed to be surveyed.

Henrik Ohlsson, Tianshi Chen, Sina Khoshfetrat Pakazad et al.

Anomaly detection in large populations is a challenging but highly relevant problem. The problem is essentially a multi-hypothesis problem, with a hypothesis for every division of the systems into normal and anomal systems. The number of hypothesis grows rapidly with the number of systems and approximate solutions become a necessity for any problems of practical interests. In the current paper we take an optimization approach to this multi-hypothesis problem. We first observe that the problem is equivalent to a non-convex combinatorial optimization problem. We then relax the problem to a convex problem that can be solved distributively on the systems and that stays computationally tractable as the number of systems increase. An interesting property of the proposed method is that it can under certain conditions be shown to give exactly the same result as the combinatorial multi-hypothesis problem and the relaxation is hence tight.

Henrik Ohlsson, Yonina C. Eldar, Allen Y. Yang et al.

The classical shift retrieval problem considers two signals in vector form that are related by a shift. The problem is of great importance in many applications and is typically solved by maximizing the cross-correlation between the two signals. Inspired by compressive sensing, in this paper, we seek to estimate the shift directly from compressed signals. We show that under certain conditions, the shift can be recovered using fewer samples and less computation compared to the classical setup. Of particular interest is shift estimation from Fourier coefficients. We show that under rather mild conditions only one Fourier coefficient suffices to recover the true shift.

Henrik Ohlsson, Allen Y. Yang, Roy Dong et al.

In many compressive sensing problems today, the relationship between the measurements and the unknowns could be nonlinear. Traditional treatment of such nonlinear relationships have been to approximate the nonlinearity via a linear model and the subsequent un-modeled dynamics as noise. The ability to more accurately characterize nonlinear models has the potential to improve the results in both existing compressive sensing applications and those where a linear approximation does not suffice, e.g., phase retrieval. In this paper, we extend the classical compressive sensing framework to a second-order Taylor expansion of the nonlinearity. Using a lifting technique and a method we call quadratic basis pursuit, we show that the sparse signal can be recovered exactly when the sampling rate is sufficiently high. We further present efficient numerical algorithms to recover sparse signals in second-order nonlinear systems, which are considerably more difficult to solve than their linear counterparts in sparse optimization.

Anil Aswani, Humberto Gonzalez, S. Shankar Sastry et al.

Learning-based model predictive control (LBMPC) is a technique that provides deterministic guarantees on robustness, while statistical identification tools are used to identify richer models of the system in order to improve performance. This technical note provides proofs that elucidate the reasons for our choice of measurement model, as well as giving proofs concerning the stochastic convergence of LBMPC. The first part of this note discusses simultaneous state estimation and statistical identification (or learning) of unmodeled dynamics, for dynamical systems that can be described by ordinary differential equations (ODE's). The second part provides proofs concerning the epi-convergence of different statistical estimators that can be used with the learning-based model predictive control (LBMPC) technique. In particular, we prove results on the statistical properties of a nonparametric estimator that we have designed to have the correct deterministic and stochastic properties for numerical implementation when used in conjunction with LBMPC.

Dheeraj Singaraju, Ehsan Elhamifar, Roberto Tron et al.

Recent results in Compressive Sensing have shown that, under certain conditions, the solution to an underdetermined system of linear equations with sparsity-based regularization can be accurately recovered by solving convex relaxations of the original problem. In this work, we present a novel primal-dual analysis on a class of sparsity minimization problems. We show that the Lagrangian bidual (i.e., the Lagrangian dual of the Lagrangian dual) of the sparsity minimization problems can be used to derive interesting convex relaxations: the bidual of the $\ell_0$-minimization problem is the $\ell_1$-minimization problem; and the bidual of the $\ell_{0,1}$-minimization problem for enforcing group sparsity on structured data is the $\ell_{1,\infty}$-minimization problem. The analysis provides a means to compute per-instance non-trivial lower bounds on the (group) sparsity of the desired solutions. In a real-world application, the bidual relaxation improves the performance of a sparsity-based classification framework applied to robust face recognition.