arXiv subjects

Tien Mai

Publications and source records attributed to Tien Mai.

40 records · Page 3Linked to original sources

arXiv2020

Generalized Maximum Causal Entropy for Inverse Reinforcement Learning

We consider the problem of learning from demonstrated trajectories with inverse reinforcement learning (IRL). Motivated by a limitation of the classical maximum entropy model in capturing the structure of the network of states, we propose an IRL model based on a generalized version of the causal entropy maximization problem, which allows us to generate a class of maximum entropy IRL models. Our generalized model has an advantage of being able to recover, in addition to a reward function, another expert's function that would (partially) capture the impact of the connecting structure of the states on experts' decisions. Empirical evaluation on a real-world dataset and a grid-world dataset shows that our generalized model outperforms the classical ones, in terms of recovering reward functions and demonstrated trajectories.

cs.LG↗

arXiv2020

A Relation Analysis of Markov Decision Process Frameworks

We study the relation between different Markov Decision Process (MDP) frameworks in the machine learning and econometrics literatures, including the standard MDP, the entropy and general regularized MDP, and stochastic MDP, where the latter is based on the assumption that the reward function is stochastic and follows a given distribution. We show that the entropy-regularized MDP is equivalent to a stochastic MDP model, and is strictly subsumed by the general regularized MDP. Moreover, we propose a distributional stochastic MDP framework by assuming that the distribution of the reward function is ambiguous. We further show that the distributional stochastic MDP is equivalent to the regularized MDP, in the sense that they always yield the same optimal policies. We also provide a connection between stochastic/regularized MDP and constrained MDP. Our work gives a unified view on several important MDP frameworks, which would lead new ways to interpret the (entropy/general) regularized MDP frameworks through the lens of stochastic rewards and vice-versa. Given the recent popularity of regularized MDP in (deep) reinforcement learning, our work brings new understandings of how such algorithmic schemes work and suggest ideas to develop new ones.

math.OC↗

arXiv2020

Modeling Route Choice with Real-Time Information: Comparing the Recursive and Non-Recursive Models

We study the routing policy choice problems in a stochastic time-dependent (STD) network. A routing policy is defined as a decision rule applied at the end of each link that maps the realized traffic condition to the decision on the link to take next. Two types of routing policy choice models are formulated with perfect online information (POI): recursive logit model and non-recursive logit model. In the non-recursive model, a choice set of routing policies between an origin-destination (OD) pair is generated, and a probabilistic choice is modeled at the origin, while the choice of the next link at each link is a deterministic execution of the chosen routing policy. In the recursive model, the probabilistic choice of the next link is modeled at each link, following the framework of dynamic discrete choice models. The two models are further compared in terms of computational efficiency in estimation and prediction, and flexibility in systematic utility specification and modeling correlation.

eess.SY↗

arXiv2019

Inverse Reinforcement Learning with Missing Data

We consider the problem of recovering an expert's reward function with inverse reinforcement learning (IRL) when there are missing/incomplete state-action pairs or observations in the demonstrated trajectories. This issue of missing trajectory data or information occurs in many situations, e.g., GPS signals from vehicles moving on a road network are intermittent. In this paper, we propose a tractable approach to directly compute the log-likelihood of demonstrated trajectories with incomplete/missing data. Our algorithm is efficient in handling a large number of missing segments in the demonstrated trajectories, as it performs the training with incomplete data by solving a sequence of systems of linear equations, and the number of such systems to be solved does not depend on the number of missing segments. Empirical evaluation on a real-world dataset shows that our training algorithm outperforms other conventional techniques.

cs.LG↗