arXiv subjects

Daniel A. Lazar

Publications and source records attributed to Daniel A. Lazar.

11 recordsLinked to original sources

arXiv2021

The Role of Differentiation in Tolling of Traffic Networks with Mixed Autonomy

With autonomous vehicles now sharing roads with human drivers, the era of mixed autonomy brings new challenges in dealing with congestion. One cause of congestion is when vehicle users choose their routes selfishly to minimize their personal travel delay rather than a global travel delay, and prior works address this phenomenon using tolling to influence routing choices, but do not address the setting of mixed autonomy. Tolls may be differentiated, meaning different users of a road experience different tolls, or they may be anonymous; the latter is desirable to allay concerns of fairness and privacy, as well as logistical challenges. In this work we examine the role of differentiation in traffic networks with mixed autonomy. Specifically, we first establish differentiated tolls which completely eliminate inefficiency due to selfish routing. We then show the fundamental limitations of anonymous tolls in our setting, and we provide anonymous tolls with mild performance guarantees. We show that in parallel networks, an infinitesimal differentiation in tolls is enough to guarantee optimality, and finally we establish a lower bound on the inefficiency of variable marginal cost tolling in the mixed autonomy setting.

math.OC↗

arXiv2021

Learning How to Dynamically Route Autonomous Vehicles on Shared Roads

Road congestion induces significant costs across the world, and road network disturbances, such as traffic accidents, can cause highly congested traffic patterns. If a planner had control over the routing of all vehicles in the network, they could easily reverse this effect. In a more realistic scenario, we consider a planner that controls autonomous cars, which are a fraction of all present cars. We study a dynamic routing game, in which the route choices of autonomous cars can be controlled and the human drivers react selfishly and dynamically. As the problem is prohibitively large, we use deep reinforcement learning to learn a policy for controlling the autonomous vehicles. This policy indirectly influences human drivers to route themselves in such a way that minimizes congestion on the network. To gauge the effectiveness of our learned policies, we establish theoretical results characterizing equilibria and empirically compare the learned policy results with best possible equilibria. We prove properties of equilibria on parallel roads and provide a polynomial-time optimization for computing the most efficient equilibrium. Moreover, we show that in the absence of these policies, high demand and network perturbations would result in large congestion, whereas using the policy greatly decreases the travel times by minimizing the congestion. To the best of our knowledge, this is the first work that employs deep reinforcement learning to reduce congestion by indirectly influencing humans' routing decisions in mixed-autonomy traffic.

math.OC↗

arXiv2021

Emergent Prosociality in Multi-Agent Games Through Gifting

Coordination is often critical to forming prosocial behaviors -- behaviors that increase the overall sum of rewards received by all agents in a multi-agent game. However, state of the art reinforcement learning algorithms often suffer from converging to socially less desirable equilibria when multiple equilibria exist. Previous works address this challenge with explicit reward shaping, which requires the strong assumption that agents can be forced to be prosocial. We propose using a less restrictive peer-rewarding mechanism, gifting, that guides the agents toward more socially desirable equilibria while allowing agents to remain selfish and decentralized. Gifting allows each agent to give some of their reward to other agents. We employ a theoretical framework that captures the benefit of gifting in converging to the prosocial equilibrium by characterizing the equilibria's basins of attraction in a dynamical system. With gifting, we demonstrate increased convergence of high risk, general-sum coordination games to the prosocial equilibrium both via numerical analysis and experiments.

cs.MA↗

arXiv2021

Incentivizing Efficient Equilibria in Traffic Networks with Mixed Autonomy

Traffic congestion has large economic and social costs. The introduction of autonomous vehicles can potentially reduce this congestion by increasing road capacity via vehicle platooning and by creating an avenue for influencing people's choice of routes. We consider a network of parallel roads with two modes of transportation: (i) human drivers, who will choose the quickest route available to them, and (ii) a ride hailing service, which provides an array of autonomous vehicle route options, each with different prices, to users. We formalize a model of vehicle flow in mixed autonomy and a model of how autonomous service users make choices between routes with different prices and latencies. Developing an algorithm to learn the preferences of the users, we formulate a planning optimization that chooses prices to maximize a social objective. We demonstrate the benefit of the proposed scheme by comparing the results to theoretical benchmarks which we show can be efficiently calculated.

cs.MA↗

arXiv2021

Incentivizing Routing Choices for Safe and Efficient Transportation in the Face of the COVID-19 Pandemic

The COVID-19 pandemic has severely affected many aspects of people's daily lives. While many countries are in a re-opening stage, some effects of the pandemic on people's behaviors are expected to last much longer, including how they choose between different transport options. Experts predict considerably delayed recovery of the public transport options, as people try to avoid crowded places. In turn, significant increases in traffic congestion are expected, since people are likely to prefer using their own vehicles or taxis as opposed to riskier and more crowded options such as the railway. In this paper, we propose to use financial incentives to set the tradeoff between risk of infection and congestion to achieve safe and efficient transportation networks. To this end, we formulate a network optimization problem to optimize taxi fares. For our framework to be useful in various cities and times of the day without much designer effort, we also propose a data-driven approach to learn human preferences about transport options, which is then used in our taxi fare optimization. Our user studies and simulation experiments show our framework is able to minimize congestion and risk of infection.

cs.SI↗

arXiv2020

Optimal Tolling for Multitype Mixed Autonomous Traffic Networks

When selfish users share a road network and minimize their individual travel costs, the equilibrium they reach can be worse than the socially optimal routing. Tolls are often used to mitigate this effect in traditional congestion games, where all vehicle contribute identically to congestion. However, with the proliferation of autonomous vehicles and driver-assistance technology, vehicles become heterogeneous in how they contribute to road latency. This magnifies the potential inefficiencies due to selfish routing and invalidates traditional tolling methods. To address this, we consider a network of parallel roads where the latency on each road is an affine function of the quantity of flow of each vehicle type. We provide tolls (which differentiate between vehicle types) which are guaranteed to minimize social cost at equilibrium. The tolls are a function of a calculated optimal routing; to enable this tolling, we prove that some element in the set of optimal routings has a lack of cycles in a graph representing the way vehicles types share roads. We then show that unless a planner can differentiate between vehicle types in the tolls given, the resulting equilibrium can be unboundedly worse than the optimal routing, and that marginal cost tolling fails in our setting.

math.OC↗

arXiv2019

Optimal Tolling for Heterogeneous Traffic Networks with Mixed Autonomy

When people pick routes to minimize their travel time, the total experienced delay, or social cost, may be significantly greater than if people followed routes assigned to them by a social planner. This effect is accentuated when human drivers share roads with autonomous vehicles. When routed optimally, autonomous vehicles can make traffic networks more efficient, but when acting selfishly, the introduction of autonomous vehicles can actually worsen congestion. We seek to mitigate this effect by influencing routing choices via tolling. We consider a network of parallel roads with affine latency functions that are heterogeneous, meaning that the increase in capacity due to to the presence of autonomous vehicles may vary from road to road. We show that if human drivers and autonomous users have the same tolls, the social cost may be arbitrarily worse than when optimally routed. We then prove qualities of the optimal routing and use them to design tolls that are guaranteed to minimize social cost at equilibrium. To the best of our knowledge, this is the first tolling scheme that yields a unique socially optimal equilibrium for parallel heterogeneous network with affine latency functions.

math.OC↗

arXiv2019

The Green Choice: Learning and Influencing Human Decisions on Shared Roads

Autonomous vehicles have the potential to increase the capacity of roads via platooning, even when human drivers and autonomous vehicles share roads. However, when users of a road network choose their routes selfishly, the resulting traffic configuration may be very inefficient. Because of this, we consider how to influence human decisions so as to decrease congestion on these roads. We consider a network of parallel roads with two modes of transportation: (i) human drivers who will choose the quickest route available to them, and (ii) ride hailing service which provides an array of autonomous vehicle ride options, each with different prices, to users. In this work, we seek to design these prices so that when autonomous service users choose from these options and human drivers selfishly choose their resulting routes, road usage is maximized and transit delay is minimized. To do so, we formalize a model of how autonomous service users make choices between routes with different price/delay values. Developing a preference-based algorithm to learn the preferences of the users, and using a vehicle flow model related to the Fundamental Diagram of Traffic, we formulate a planning optimization to maximize a social objective and demonstrate the benefit of the proposed routing and learning scheme.

math.OC↗

arXiv2018

Maximizing Road Capacity Using Cars that Influence People

The emerging technology enabling autonomy in vehicles has led to a variety of new problems in transportation networks, such as planning and perception for autonomous vehicles. Other works consider social objectives such as decreasing fuel consumption and travel time by platooning. However, these strategies are limited by the actions of the surrounding human drivers. In this paper, we consider proactively achieving these social objectives by influencing human behavior through planned interactions. Our key insight is that we can use these social objectives to design local interactions that influence human behavior to achieve these goals. To this end, we characterize the increase in road capacity afforded by platooning, as well as the vehicle configuration that maximizes road capacity. We present a novel algorithm that uses a low-level control framework to leverage local interactions to optimally rearrange vehicles. We showcase our algorithm using a simulated road shared between autonomous and human-driven vehicles, in which we illustrate the reordering in action.

math.OC↗

arXiv2018

Routing for Traffic Networks with Mixed Autonomy

In this work we propose a macroscopic model for studying routing on networks shared between human-driven and autonomous vehicles that captures the effects of autonomous vehicles forming platoons. We use this to study inefficiency due to selfish routing and bound the Price of Anarchy (PoA), the maximum ratio between total delay experienced by selfish users and the minimum possible total delay. To do so, we establish two road capacity models, each corresponding to an assumption regarding the platooning capabilities of autonomous vehicles. Using these we develop a class of road delay functions, parameterized by the road capacity, that are polynomial with respect to vehicle flow. We then bound the PoA and the bicriteria, another measure of the inefficiency due to selfish routing. We find these bounds depend on: 1) the degree of the polynomial in the road cost function and 2) the degree of asymmetry, the difference in how human-driven and autonomous traffic affect congestion. We demonstrate that these bounds recover the classical bounds when no asymmetry exists. We show the bounds are tight in certain cases and that the PoA bound is order-optimal with respect to the degree of asymmetry.

math.OC↗

arXiv2017

The Price of Anarchy for Transportation Networks with Mixed Autonomy

We study routing behavior in transportation networks with mixed autonomy, that is, networks in which a fraction of the vehicles on each road are equipped with autonomous capabilities such as adaptive cruise control that enable reduced headways and increased road capacity. Motivated by capacity models developed for such roads with mixed autonomy, we consider transportation networks in which the delay on each road or link is an affine function of two quantities: the number of vehicles with autonomous capabilities on the link and the number of regular vehicles on the link. We particularly study the price of anarchy for such networks, that is, the ratio of the total delay experienced by selfish routing to the socially optimal routing policy. Unlike the case when all vehicles are of the same type, for which the price of anarchy is known to be bounded, we first show that the price of anarchy can be arbitrarily large for such mixed autonomous networks. Next, we define a notion of asymmetry equal to the maximum possible travel time improvement due to the presence of autonomous vehicles. We show that when the degree of asymmetry of all links in the network is bounded by a factor less than 4, the price of anarchy is bounded. We also bound the bicriteria, which is a bound on the cost of selfishly routing traffic compared to the cost of optimally routing additional traffic. These bounds depend on the degree of asymmetry and recover classical bounds on the price of anarchy and bicriteria in the case when no asymmetry exists. Further, we show with examples that these bound are tight in particular cases.

math.OC↗