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Partially observable Markov decision processes (POMDPs) provide a flexible representation for real-world decision and control problems. However, POMDPs are notoriously difficult to solve, especially when the state and observation spaces are continuous or hybrid, which is often the case for physical systems. While recent online sampling-based POMDP algorithms that plan with observation likelihood weighting have shown practical effectiveness, a general theory characterizing the approximation error of the particle filtering techniques that these algorithms use has not previously been proposed. Our main contribution is bounding the error between any POMDP and its corresponding finite sample particle belief MDP (PB-MDP) approximation. This fundamental bridge between PB-MDPs and POMDPs allows us to adapt any sampling-based MDP algorithm to a POMDP by solving the corresponding particle belief MDP, thereby extending the convergence guarantees of the MDP algorithm to the POMDP. Practically, this is implemented by using the particle filter belief transition model as the generative model for the MDP solver. While this requires access to the observation density model from the POMDP, it only increases the transition sampling complexity of the MDP solver by a factor of O(C), where C is the number of particles. Thus, when combined with sparse sampling MDP algorithms, this approach can yield algorithms for POMDPs that have no direct theoretical dependence on the size of the state and observation spaces. In addition to our theoretical contribution, we perform five numerical experiments on benchmark POMDPs to demonstrate that a simple MDP algorithm adapted using PB-MDP approximation, Sparse-PFT, achieves performance competitive with other leading continuous observation POMDP solvers.

 

Designing reward functions is a difficult task in AI and robotics. The complex task of directly specifying all the desirable behaviors a robot needs to optimize often proves challenging for humans. A popular solution is to learn reward functions using expert demonstrations. This approach, however, is fraught with many challenges. Some methods require heavily structured models, for example, reward functions that are linear in some predefined set of features, while others adopt less structured reward functions that may necessitate tremendous amounts of data. Moreover, it is difficult for humans to provide demonstrations on robots with high degrees of freedom, or even quantifying reward values for given trajectories. To address these challenges, we present a preference-based learning approach, where human feedback is in the form of comparisons between trajectories. We do not assume highly constrained structures on the reward function. Instead, we employ a Gaussian process to model the reward function and propose a mathematical formulation to actively fit the model using only human preferences. Our approach enables us to tackle both inflexibility and data-inefficiency problems within a preference-based learning framework. We further analyze our algorithm in comparison to several baselines on reward optimization, where the goal is to find the optimal robot trajectory in a data-efficient way instead of learning the reward function for every possible trajectory. Our results in three different simulation experiments and a user study show our approach can efficiently learn expressive reward functions for robotic tasks, and outperform the baselines in both reward learning and reward optimization.

 

Neural networks can learn complex, non-convex functions, and it is challenging to guarantee their correct behavior in safety-critical contexts. Many approaches exist to find failures in networks (e.g., adversarial examples), but these cannot guarantee the absence of failures. Verification algorithms address this need and provide formal guarantees about a neural network by answering "yes or no" questions. For example, they can answer whether a violation exists within certain bounds. However, individual "yes or no" questions cannot answer qualitative questions such as “what is the largest error within these bounds”; the answers to these lie in the domain of optimization. Therefore, we propose strategies to extend existing verifiers to perform optimization and find: (i) the most extreme failure in a given input region and (ii) the minimum input perturbation required to cause a failure. A naive approach using a bisection search with an off-the-shelf verifier results in many expensive and overlapping calls to the verifier. Instead, we propose an approach that tightly integrates the optimization process into the verification procedure, achieving better runtime performance than the naive approach. We evaluate our approach implemented as an extension of Marabou, a state-of-the-art neural network verifier, and compare its performance with the bisection approach and MIPVerify, an optimization-based verifier. We observe complementary performance between our extension of Marabou and MIPVerify 

Physical inactivity is the fourth leading cause of global mortality. Health organizations have requested a tool to objectively measure physical activity. Respirometry and doubly labeled water accurately estimate energy expenditure, but are infeasible for everyday use. Smartwatches are portable, but have significant errors. Existing wearable methods poorly estimate time-varying activity, which comprises 40% of daily steps. Here, we present a Wearable System that estimates metabolic energy expenditure in real-time during common steady-state and time-varying activities with substantially lower error than state-of-the-art methods. We perform experiments to select sensors, collect training data, and validate the Wearable System with new subjects and new conditions for walking, running, stair climbing, and biking. The Wearable System uses inertial measurement units worn on the shank and thigh as they distinguish lower-limb activity better than wrist or trunk kinematics and converge more quickly than physiological signals. When evaluated with a diverse group of new subjects, the Wearable System has a cumulative error of 13% across common activities, significantly less than 42% for a smartwatch and 44% for an activity-specific smartwatch. This approach enables accurate physical activity monitoring which could enable new energy balance systems for weight management or large-scale activity monitoring.

 

We consider the problem of routing a large fleet of drones to deliver packages simultaneously across broad urban areas. Besides flying directly, drones can use public transit vehicles such as buses and trams as temporary modes of transportation to conserve energy. Adding this capability to our formulation augments effective drone travel range and the space of possible deliveries but also increases problem input size due to the large transit networks. We present a comprehensive algorithmic framework that strives to minimize the maximum time to complete any delivery and addresses the multifaceted computational challenges of our problem through a two-layer approach. First, the upper layer assigns drones to package delivery sequences with an approximately optimal polynomial time allocation algorithm. Then, the lower layer executes the allocation by periodically routing the fleet over the transit network, using efficient, bounded suboptimal multi-agent pathfinding techniques tailored to our setting. We demonstrate the efficiency of our approach on simulations with up to 200 drones, 5000 packages, and transit networks with up to 8000 stops in San Francisco and the Washington DC Metropolitan Area. Our framework computes solutions for most settings within a few seconds on commodity hardware and enables drones to extend their effective range by a factor of nearly four using transit. 

A classical problem in city-scale cyber-physical systems (CPS) is resource allocation under uncertainty. Spatial-temporal allocation of resources is optimized to allocate electric scooters across urban areas, place charging stations for vehicles, and design efficient on-demand transit. Typically, such problems are modeled as Markov (or semi-Markov) decision processes. While online, offline, and decentralized methodologies have been used to tackle such problems, none of the approaches scale well for large-scale decision problems. We create a general approach to hierarchical planning that leverages structure in city-level CPS problems to tackle resource allocation under uncertainty. We use emergency response as a case study and show how a large resource allocation problem can be split into smaller problems. We then create a principled framework for solving the smaller problems and tackling the interaction between them. Finally, we use real-world data from a major metropolitan area in the United States to validate our approach. Our experiments show that the proposed approach outperforms state-of-the-art approaches used in the field of emergency response.