Sushmita Bhattacharya

Daniel Garces, Sushmita Bhattacharya, Stephanie Gil et al.

We derive a learning framework to generate routing/pickup policies for a fleet of autonomous vehicles tasked with servicing stochastically appearing requests on a city map. We focus on policies that 1) give rise to coordination amongst the vehicles, thereby reducing wait times for servicing requests, 2) are non-myopic, and consider a-priori potential future requests, 3) can adapt to changes in the underlying demand distribution. Specifically, we are interested in policies that are adaptive to fluctuations of actual demand conditions in urban environments, such as on-peak vs. off-peak hours. We achieve this through a combination of (i) an online play algorithm that improves the performance of an offline-trained policy, and (ii) an offline approximation scheme that allows for adapting to changes in the underlying demand model. In particular, we achieve adaptivity of our learned policy to different demand distributions by quantifying a region of validity using the q-valid radius of a Wasserstein Ambiguity Set. We propose a mechanism for switching the originally trained offline approximation when the current demand is outside the original validity region. In this case, we propose to use an offline architecture, trained on a historical demand model that is closer to the current demand in terms of Wasserstein distance. We learn routing and pickup policies over real taxicab requests in San Francisco with high variability between on-peak and off-peak hours, demonstrating the ability of our method to adapt to real fluctuation in demand distributions. Our numerical results demonstrate that our method outperforms alternative rollout-based reinforcement learning schemes, as well as other classical methods from operations research.

Daniel Garces, Sushmita Bhattacharya, Dimitri Bertsekas et al.

In this paper, we focus on the autonomous multiagent taxi routing problem for a large urban environment where the location and number of future ride requests are unknown a-priori, but can be estimated by an empirical distribution. Recent theory has shown that a rollout algorithm with a stable base policy produces a near-optimal stable policy. In the routing setting, a policy is stable if its execution keeps the number of outstanding requests uniformly bounded over time. Although, rollout-based approaches are well-suited for learning cooperative multiagent policies with considerations for future demand, applying such methods to a large urban environment can be computationally expensive due to the large number of taxis required for stability. In this paper, we aim to address the computational bottleneck of multiagent rollout by proposing an approximate multiagent rollout-based two phase algorithm that reduces computational costs, while still achieving a stable near-optimal policy. Our approach partitions the graph into sectors based on the predicted demand and the maximum number of taxis that can run sequentially given the user's computational resources. The algorithm then applies instantaneous assignment (IA) for re-balancing taxis across sectors and a sector-wide multiagent rollout algorithm that is executed in parallel for each sector. We provide two main theoretical results: 1) characterize the number of taxis $m$ that is sufficient for IA to be stable; 2) derive a necessary condition on $m$ to maintain stability for IA as time goes to infinity. Our numerical results show that our approach achieves stability for an $m$ that satisfies the theoretical conditions. We also empirically demonstrate that our proposed two phase algorithm has equivalent performance to the one-at-a-time rollout over the entire map, but with significantly lower runtimes.

Sushmita Bhattacharya, Siva Kailas, Sahil Badyal et al.

In this paper we consider infinite horizon discounted dynamic programming problems with finite state and control spaces, partial state observations, and a multiagent structure. We discuss and compare algorithms that simultaneously or sequentially optimize the agents' controls by using multistep lookahead, truncated rollout with a known base policy, and a terminal cost function approximation. Our methods specifically address the computational challenges of partially observable multiagent problems. In particular: 1) We consider rollout algorithms that dramatically reduce required computation while preserving the key cost improvement property of the standard rollout method. The per-step computational requirements for our methods are on the order of $O(Cm)$ as compared with $O(C^m)$ for standard rollout, where $C$ is the maximum cardinality of the constraint set for the control component of each agent, and $m$ is the number of agents. 2) We show that our methods can be applied to challenging problems with a graph structure, including a class of robot repair problems whereby multiple robots collaboratively inspect and repair a system under partial information. 3) We provide a simulation study that compares our methods with existing methods, and demonstrate that our methods can handle larger and more complex partially observable multiagent problems (state space size $10^{37}$ and control space size $10^{7}$, respectively). Finally, we incorporate our multiagent rollout algorithms as building blocks in an approximate policy iteration scheme, where successive rollout policies are approximated by using neural network classifiers. While this scheme requires a strictly off-line implementation, it works well in our computational experiments and produces additional significant performance improvement over the single online rollout iteration method.

Sushmita Bhattacharya, Sahil Badyal, Thomas Wheeler et al.

In this paper we consider infinite horizon discounted dynamic programming problems with finite state and control spaces, and partial state observations. We discuss an algorithm that uses multistep lookahead, truncated rollout with a known base policy, and a terminal cost function approximation. This algorithm is also used for policy improvement in an approximate policy iteration scheme, where successive policies are approximated by using a neural network classifier. A novel feature of our approach is that it is well suited for distributed computation through an extended belief space formulation and the use of a partitioned architecture, which is trained with multiple neural networks. We apply our methods in simulation to a class of sequential repair problems where a robot inspects and repairs a pipeline with potentially several rupture sites under partial information about the state of the pipeline.