J. Michael Harrison

Baris Ata, J. Michael Harrison, Nian Si

Motivated by applications in queueing theory, we consider a stochastic control problem whose state space is the $d$-dimensional positive orthant. The controlled process $Z$ evolves as a reflected Brownian motion whose covariance matrix is exogenously specified, as are its directions of reflection from the orthant's boundary surfaces. A system manager chooses a drift vector $θ(t)$ at each time $t$ based on the history of $Z$, and the cost rate at time $t$ depends on both $Z(t)$ and $θ(t)$. In our initial problem formulation, the objective is to minimize expected discounted cost over an infinite planning horizon, after which we treat the corresponding ergodic control problem. Extending earlier work by Han et al. (Proceedings of the National Academy of Sciences, 2018, 8505-8510), we develop and illustrate a simulation-based computational method that relies heavily on deep neural network technology. For test problems studied thus far, our method is accurate to within a fraction of one percent, and is computationally feasible in dimensions up to at least $d=30$.

Robert Dyro, James Harrison, Apoorva Sharma et al.

As robotic systems move from highly structured environments to open worlds, incorporating uncertainty from dynamics learning or state estimation into the control pipeline is essential for robust performance. In this paper we present a nonlinear particle model predictive control (PMPC) approach to control under uncertainty, which directly incorporates any particle-based uncertainty representation, such as those common in robotics. Our approach builds on scenario methods for MPC, but in contrast to existing approaches, which either constrain all or only the first timestep to share actions across scenarios, we investigate the impact of a \textit{partial consensus horizon}. Implementing this optimization for nonlinear dynamics by leveraging sequential convex optimization, our approach yields an efficient framework that can be tuned to the particular information gain dynamics of a system to mitigate both over-conservatism and over-optimism. We investigate our approach for two robotic systems across three problem settings: time-varying, partially observed dynamics; sensing uncertainty; and model-based reinforcement learning, and show that our approach improves performance over baselines in all settings.

S. Banerjee, J. Harrison, P. M. Furlong et al.

Rovers require knowledge of terrain to plan trajectories that maximize safety and efficiency. Terrain type classification relies on input from human operators or machine learning-based image classification algorithms. However, high level terrain classification is typically not sufficient to prevent incidents such as rovers becoming unexpectedly stuck in a sand trap; in these situations, online rover-terrain interaction data can be leveraged to accurately predict future dynamics and prevent further damage to the rover. This paper presents a meta-learning-based approach to adapt probabilistic predictions of rover dynamics by augmenting a nominal model affine in parameters with a Bayesian regression algorithm (P-ALPaCA). A regularization scheme is introduced to encourage orthogonality of nominal and learned features, leading to interpretable probabilistic estimates of terrain parameters in varying terrain conditions.

Annie Xie, James Harrison, Chelsea Finn

As humans, our goals and our environment are persistently changing throughout our lifetime based on our experiences, actions, and internal and external drives. In contrast, typical reinforcement learning problem set-ups consider decision processes that are stationary across episodes. Can we develop reinforcement learning algorithms that can cope with the persistent change in the former, more realistic problem settings? While on-policy algorithms such as policy gradients in principle can be extended to non-stationary settings, the same cannot be said for more efficient off-policy algorithms that replay past experiences when learning. In this work, we formalize this problem setting, and draw upon ideas from the online learning and probabilistic inference literature to derive an off-policy RL algorithm that can reason about and tackle such lifelong non-stationarity. Our method leverages latent variable models to learn a representation of the environment from current and past experiences, and performs off-policy RL with this representation. We further introduce several simulation environments that exhibit lifelong non-stationarity, and empirically find that our approach substantially outperforms approaches that do not reason about environment shift.

James Harrison, Apoorva Sharma, Chelsea Finn et al.

Meta-learning is a promising strategy for learning to efficiently learn within new tasks, using data gathered from a distribution of tasks. However, the meta-learning literature thus far has focused on the task segmented setting, where at train-time, offline data is assumed to be split according to the underlying task, and at test-time, the algorithms are optimized to learn in a single task. In this work, we enable the application of generic meta-learning algorithms to settings where this task segmentation is unavailable, such as continual online learning with a time-varying task. We present meta-learning via online changepoint analysis (MOCA), an approach which augments a meta-learning algorithm with a differentiable Bayesian changepoint detection scheme. The framework allows both training and testing directly on time series data without segmenting it into discrete tasks. We demonstrate the utility of this approach on a nonlinear meta-regression benchmark as well as two meta-image-classification benchmarks.

Apoorva Sharma, James Harrison, Matthew Tsao et al.

Planning under model uncertainty is a fundamental problem across many applications of decision making and learning. In this paper, we propose the Robust Adaptive Monte Carlo Planning (RAMCP) algorithm, which allows computation of risk-sensitive Bayes-adaptive policies that optimally trade off exploration, exploitation, and robustness. RAMCP formulates the risk-sensitive planning problem as a two-player zero-sum game, in which an adversary perturbs the agent's belief over the models. We introduce two versions of the RAMCP algorithm. The first, RAMCP-F, converges to an optimal risk-sensitive policy without having to rebuild the search tree as the underlying belief over models is perturbed. The second version, RAMCP-I, improves computational efficiency at the cost of losing theoretical guarantees, but is shown to yield empirical results comparable to RAMCP-F. RAMCP is demonstrated on an n-pull multi-armed bandit problem, as well as a patient treatment scenario.

James Harrison, Apoorva Sharma, Marco Pavone

Gaussian Process (GP) regression has seen widespread use in robotics due to its generality, simplicity of use, and the utility of Bayesian predictions. The predominant implementation of GP regression is a nonparameteric kernel-based approach, as it enables fitting of arbitrary nonlinear functions. However, this approach suffers from two main drawbacks: (1) it is computationally inefficient, as computation scales poorly with the number of samples; and (2) it can be data inefficient, as encoding prior knowledge that can aid the model through the choice of kernel and associated hyperparameters is often challenging and unintuitive. In this work, we propose ALPaCA, an algorithm for efficient Bayesian regression which addresses these issues. ALPaCA uses a dataset of sample functions to learn a domain-specific, finite-dimensional feature encoding, as well as a prior over the associated weights, such that Bayesian linear regression in this feature space yields accurate online predictions of the posterior predictive density. These features are neural networks, which are trained via a meta-learning (or "learning-to-learn") approach. ALPaCA extracts all prior information directly from the dataset, rather than restricting prior information to the choice of kernel hyperparameters. Furthermore, by operating in the weight space, it substantially reduces sample complexity. We investigate the performance of ALPaCA on two simple regression problems, two simulated robotic systems, and on a lane-change driving task performed by humans. We find our approach outperforms kernel-based GP regression, as well as state of the art meta-learning approaches, thereby providing a promising plug-in tool for many regression tasks in robotics where scalability and data-efficiency are important.

Brian Ichter, James Harrison, Marco Pavone

A defining feature of sampling-based motion planning is the reliance on an implicit representation of the state space, which is enabled by a set of probing samples. Traditionally, these samples are drawn either probabilistically or deterministically to uniformly cover the state space. Yet, the motion of many robotic systems is often restricted to "small" regions of the state space, due to, for example, differential constraints or collision-avoidance constraints. To accelerate the planning process, it is thus desirable to devise non-uniform sampling strategies that favor sampling in those regions where an optimal solution might lie. This paper proposes a methodology for non-uniform sampling, whereby a sampling distribution is learned from demonstrations, and then used to bias sampling. The sampling distribution is computed through a conditional variational autoencoder, allowing sample generation from the latent space conditioned on the specific planning problem. This methodology is general, can be used in combination with any sampling-based planner, and can effectively exploit the underlying structure of a planning problem while maintaining the theoretical guarantees of sampling-based approaches. Specifically, on several planning problems, the proposed methodology is shown to effectively learn representations for the relevant regions of the state space, resulting in an order of magnitude improvement in terms of success rate and convergence to the optimal cost.