Markov Models
A Software Architecture for Autonomous Vehicles: Team LRM-B Entry in the First CARLA Autonomous Driving Challenge
Rosero, Luis Alberto, Gomes, Iago Pacheco, da Silva, Jรบnior Anderson Rodrigues, Santos, Tiago Cesar dos, Nakamura, Angelica Tiemi Mizuno, Amaro, Jean, Wolf, Denis Fernando, Osรณrio, Fernando Santos
The objective of the first CARLA autonomous driving challenge was to deploy autonomous driving systems to lead with complex traffic scenarios where all participants faced the same challenging traffic situations. According to the organizers, this competition emerges as a way to democratize and to accelerate the research and development of autonomous vehicles around the world using the CARLA simulator contributing to the development of the autonomous vehicle area. Therefore, this paper presents the architecture design for the navigation of an autonomous vehicle in a simulated urban environment that attempts to commit the least number of traffic infractions, which used as the baseline the original architecture of the platform for autonomous navigation CaRINA 2. Our agent traveled in simulated scenarios for several hours, demonstrating his capabilities, winning three out of the four tracks of the challenge, and being ranked second in the remaining track. Our architecture was made towards meeting the requirements of CARLA Autonomous Driving Challenge and has components for obstacle detection using 3D point clouds, traffic signs detection and classification which employs Convolutional Neural Networks (CNN) and depth information, risk assessment with collision detection using short-term motion prediction, decision-making with Markov Decision Process (MDP), and control using Model Predictive Control (MPC).
Multi-agent active perception with prediction rewards
Lauri, Mikko, Oliehoek, Frans A.
Multi-agent active perception is a task where a team of agents cooperatively gathers observations to compute a joint estimate of a hidden variable. The task is decentralized and the joint estimate can only be computed after the task ends by fusing observations of all agents. The objective is to maximize the accuracy of the estimate. The accuracy is quantified by a centralized prediction reward determined by a centralized decision-maker who perceives the observations gathered by all agents after the task ends. In this paper, we model multi-agent active perception as a decentralized partially observable Markov decision process (Dec-POMDP) with a convex centralized prediction reward. We prove that by introducing individual prediction actions for each agent, the problem is converted into a standard Dec-POMDP with a decentralized prediction reward. The loss due to decentralization is bounded, and we give a sufficient condition for when it is zero. Our results allow application of any Dec-POMDP solution algorithm to multi-agent active perception problems, and enable planning to reduce uncertainty without explicit computation of joint estimates. We demonstrate the empirical usefulness of our results by applying a standard Dec-POMDP algorithm to multi-agent active perception problems, showing increased scalability in the planning horizon.
Conditional independence by typing
Gorinova, Maria I., Gordon, Andrew D., Sutton, Charles, Vakar, Matthijs
A central goal of probabilistic programming languages (PPLs) is to separate modelling from inference. However, this goal is hard to achieve in practice. Users are often forced to re-write their models in order to improve efficiency of inference or meet restrictions imposed by the PPL. Conditional independence (CI) relationships among parameters are a crucial aspect of probabilistic models that captures a qualitative summary of the specified model and can facilitate more efficient inference. We present an information flow type system for probabilistic programming that captures conditional independence (CI) relationships, and show that, for a well-typed program in our system, the distribution it implements is guaranteed to have certain CI-relationships. Further, by using type inference, we can statically \emph{deduce} which CI-properties are present in a specified model. As a practical application, we consider the problem of how to perform inference on models with mixed discrete and continuous parameters. Inference on such models is challenging in many existing PPLs, but can be improved through a workaround, where the discrete parameters are used \textit{implicitly}, at the expense of manual model re-writing. We present a source-to-source semantics-preserving transformation, which uses our CI-type system to automate this workaround by eliminating the discrete parameters from a probabilistic program. The resulting program can be seen as a hybrid inference algorithm on the original program, where continuous parameters can be drawn using efficient gradient-based inference methods, while the discrete parameters are drawn using variable elimination. We implement our CI-type system and its example application in SlicStan: a compositional variant of Stan.
Global optimality of softmax policy gradient with single hidden layer neural networks in the mean-field regime
We study the problem of policy optimization for infinite-horizon discounted Markov Decision Processes with softmax policy and nonlinear function approximation trained with policy gradient algorithms. We concentrate on the training dynamics in the mean-field regime, modeling e.g., the behavior of wide single hidden layer neural networks, when exploration is encouraged through entropy regularization. The dynamics of these models is established as a Wasserstein gradient flow of distributions in parameter space. We further prove global optimality of the fixed points of this dynamics under mild conditions on their initialization.
Reversible Jump PDMP Samplers for Variable Selection
Chevallier, Augustin, Fearnhead, Paul, Sutton, Matthew
A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic Markov processes (PDMPs), have recently shown great promise: they are non-reversible, can mix better than standard MCMC algorithms, and can use subsampling ideas to speed up computation in big data scenarios. However, current PDMP samplers can only sample from posterior densities that are differentiable almost everywhere, which precludes their use for model choice. Motivated by variable selection problems, we show how to develop reversible jump PDMP samplers that can jointly explore the discrete space of models and the continuous space of parameters. Our framework is general: it takes any existing PDMP sampler, and adds two types of trans-dimensional moves that allow for the addition or removal of a variable from the model. We show how the rates of these trans-dimensional moves can be calculated so that the sampler has the correct invariant distribution. Simulations show that the new samplers can mix better than standard MCMC algorithms. Our empirical results show they are also more efficient than gradient-based samplers that avoid model choice through use of continuous spike-and-slab priors which replace a point mass at zero for each parameter with a density concentrated around zero.
CoinDICE: Off-Policy Confidence Interval Estimation
Dai, Bo, Nachum, Ofir, Chow, Yinlam, Li, Lihong, Szepesvรกri, Csaba, Schuurmans, Dale
We study high-confidence behavior-agnostic off-policy evaluation in reinforcement learning, where the goal is to estimate a confidence interval on a target policy's value, given only access to a static experience dataset collected by unknown behavior policies. Starting from a function space embedding of the linear program formulation of the $Q$-function, we obtain an optimization problem with generalized estimating equation constraints. By applying the generalized empirical likelihood method to the resulting Lagrangian, we propose CoinDICE, a novel and efficient algorithm for computing confidence intervals. Theoretically, we prove the obtained confidence intervals are valid, in both asymptotic and finite-sample regimes. Empirically, we show in a variety of benchmarks that the confidence interval estimates are tighter and more accurate than existing methods.
The Role of Mutual Information in Variational Classifiers
Vera, Matias, Vega, Leonardo Rey, Piantanida, Pablo
Overfitting data is a well-known phenomenon related with the generation of a model that mimics too closely (or exactly) a particular instance of data, and may therefore fail to predict future observations reliably. In practice, this behaviour is controlled by various--sometimes heuristics--regularization techniques, which are motivated by developing upper bounds to the generalization error. In this work, we study the generalization error of classifiers relying on stochastic encodings trained on the cross-entropy loss, which is often used in deep learning for classification problems. We derive bounds to the generalization error showing that there exists a regime where the generalization error is bounded by the mutual information between input features and the corresponding representations in the latent space, which are randomly generated according to the encoding distribution. Our bounds provide an information-theoretic understanding of generalization in the so-called class of variational classifiers, which are regularized by a Kullback-Leibler (KL) divergence term. These results give theoretical grounds for the highly popular KL term in variational inference methods that was already recognized to act effectively as a regularization penalty. We further observe connections with well studied notions such as Variational Autoencoders, Information Dropout, Information Bottleneck and Boltzmann Machines. Finally, we perform numerical experiments on MNIST and CIFAR datasets and show that mutual information is indeed highly representative of the behaviour of the generalization error.
Model updating after interventions paradoxically introduces bias
Liley, James, Emerson, Samuel R, Mateen, Bilal A, Vallejos, Catalina A, Aslett, Louis J M, Vollmer, Sebastian J
Machine learning is increasingly being used to generate prediction models for use in a number of real-world settings, from credit risk assessment to clinical decision support. Recent discussions have highlighted potential problems in the updating of a predictive score for a binary outcome when an existing predictive score forms part of the standard workflow, driving interventions. In this setting, the existing score induces an additional causative pathway which leads to miscalibration when the original score is replaced. We propose a general causal framework to describe and address this problem, and demonstrate an equivalent formulation as a partially observed Markov decision process. We use this model to demonstrate the impact of such `naive updating' when performed repeatedly. Namely, we show that successive predictive scores may converge to a point where they predict their own effect, or may eventually oscillate between two values, and we argue that neither outcome is desirable. Furthermore, we demonstrate that even if model-fitting procedures improve, actual performance may worsen. We complement these findings with a discussion of several potential routes to overcome these problems.
Weighted QMIX: Expanding Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning
Rashid, Tabish, Farquhar, Gregory, Peng, Bei, Whiteson, Shimon
QMIX is a popular $Q$-learning algorithm for cooperative MARL in the centralised training and decentralised execution paradigm. In order to enable easy decentralisation, QMIX restricts the joint action $Q$-values it can represent to be a monotonic mixing of each agent's utilities. However, this restriction prevents it from representing value functions in which an agent's ordering over its actions can depend on other agents' actions. To analyse this representational limitation, we first formalise the objective QMIX optimises, which allows us to view QMIX as an operator that first computes the $Q$-learning targets and then projects them into the space representable by QMIX. This projection returns a representable $Q$-value that minimises the unweighted squared error across all joint actions. We show in particular that this projection can fail to recover the optimal policy even with access to $Q^*$, which primarily stems from the equal weighting placed on each joint action. We rectify this by introducing a weighting into the projection, in order to place more importance on the better joint actions. We propose two weighting schemes and prove that they recover the correct maximal action for any joint action $Q$-values, and therefore for $Q^*$ as well. Based on our analysis and results in the tabular setting, we introduce two scalable versions of our algorithm, Centrally-Weighted (CW) QMIX and Optimistically-Weighted (OW) QMIX and demonstrate improved performance on both predator-prey and challenging multi-agent StarCraft benchmark tasks.
Migratable AI: Personalizing Dialog Conversations with migration context
Tejwani, Ravi, Katz, Boris, Breazeal, Cynthia
The migration of conversational AI agents across different embodiments in order to maintain the continuity of the task has been recently explored to further improve user experience. However, these migratable agents lack contextual understanding of the user information and the migrated device during the dialog conversations with the user. This opens the question of how an agent might behave when migrated into an embodiment for contextually predicting the next utterance. We collected a dataset from the dialog conversations between crowdsourced workers with the migration context involving personal and non-personal utterances in different settings (public or private) of embodiment into which the agent migrated. We trained the generative and information retrieval models on the dataset using with and without migration context and report the results of both qualitative metrics and human evaluation. We believe that the migration dataset would be useful for training future migratable AI systems.