Matthew Tsao

Matthew Tsao, Ramon Iglesias, Marco Pavone

This paper presents a stochastic, model predictive control (MPC) algorithm that leverages short-term probabilistic forecasts for dispatching and rebalancing Autonomous Mobility-on-Demand systems (AMoD, i.e. fleets of self-driving vehicles). We first present the core stochastic optimization problem in terms of a time-expanded network flow model. Then, to ameliorate its tractability, we present two key relaxations. First, we replace the original stochastic problem with a Sample Average Approximation (SAA), and characterize the performance guarantees. Second, we separate the controller into two separate parts to address the task of assigning vehicles to the outstanding customers separate from that of rebalancing. This enables the problem to be solved as two totally unimodular linear programs, and thus easily scalable to large problem sizes. Finally, we test the proposed algorithm in two scenarios based on real data and show that it outperforms prior state-of-the-art algorithms. In particular, in a simulation using customer data from DiDi Chuxing, the algorithm presented here exhibits a 62.3 percent reduction in customer waiting time compared to state of the art non-stochastic algorithms.

Matthew Tsao, Kaidi Yang, Karthik Gopalakrishnan et al.

Data-driven methodologies offer many exciting upsides, but they also introduce new challenges, particularly in the realm of user privacy. Specifically, the way data is collected can pose privacy risks to end users. In many routing services, a single entity (e.g., the routing service provider) collects and manages user trajectory data. When it comes to user privacy, these systems have a central point of failure since users have to trust that this entity will not sell or use their data to infer sensitive private information. Unfortunately, in practice many advertising companies offer to buy such data for the sake of targeted advertisements. With this as motivation, we study the problem of using location data for routing services in a privacy-preserving way. Rather than having users report their location to a central operator, we present a protocol in which users participate in a decentralized and privacy-preserving computation to estimate travel times for the roads in the network in a way that no individuals' location is ever observed by any other party. The protocol uses the Laplace mechanism in conjunction with secure multi-party computation to ensure that it is cryptogrpahically secure and that its output is differentially private. A natural question is if privacy necessitates degradation in accuracy or system performance. We show that if a road has sufficiently high capacity, then the travel time estimated by our protocol is provably close to the ground truth travel time. We validate the protocol through numerical experiments which show that using the protocol as a routing service provides privacy guarantees with minimal overhead to user travel time.

Matthew Tsao, Kiril Solovey, Marco Pavone

We study fundamental theoretical aspects of probabilistic roadmaps (PRM) in the finite time (non-asymptotic) regime. In particular, we investigate how completeness and optimality guarantees of the approach are influenced by the underlying deterministic sampling distribution ${\mathcal{X}}$ and connection radius ${r>0}$. We develop the notion of ${(δ,ε)}$-completeness of the parameters ${\mathcal{X}, r}$, which indicates that for every motion-planning problem of clearance at least ${δ>0}$, PRM using ${\mathcal{X}, r}$ returns a solution no longer than ${1+ε}$ times the shortest $δ$-clear path. Leveraging the concept of $ε$-nets, we characterize in terms of lower and upper bounds the number of samples needed to guarantee ${(δ,ε)}$-completeness. This is in contrast with previous work which mostly considered the asymptotic regime in which the number of samples tends to infinity. In practice, we propose a sampling distribution inspired by $ε$-nets that achieves nearly the same coverage as grids while using significantly fewer samples.

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.