arXiv subjects

Michael L. Littman

Publications and source records attributed to Michael L. Littman.

At least 37 records · Page 2Linked to original sources

arXiv2021

Lipschitz Lifelong Reinforcement Learning

We consider the problem of knowledge transfer when an agent is facing a series of Reinforcement Learning (RL) tasks. We introduce a novel metric between Markov Decision Processes (MDPs) and establish that close MDPs have close optimal value functions. Formally, the optimal value functions are Lipschitz continuous with respect to the tasks space. These theoretical results lead us to a value-transfer method for Lifelong RL, which we use to build a PAC-MDP algorithm with improved convergence rate. Further, we show the method to experience no negative transfer with high probability. We illustrate the benefits of the method in Lifelong RL experiments.

cs.LG↗

arXiv2021

Deep Radial-Basis Value Functions for Continuous Control

A core operation in reinforcement learning (RL) is finding an action that is optimal with respect to a learned value function. This operation is often challenging when the learned value function takes continuous actions as input. We introduce deep radial-basis value functions (RBVFs): value functions learned using a deep network with a radial-basis function (RBF) output layer. We show that the maximum action-value with respect to a deep RBVF can be approximated easily and accurately. Moreover, deep RBVFs can represent any true value function owing to their support for universal function approximation. We extend the standard DQN algorithm to continuous control by endowing the agent with a deep RBVF. We show that the resultant agent, called RBF-DQN, significantly outperforms value-function-only baselines, and is competitive with state-of-the-art actor-critic algorithms.

cs.LG↗

arXiv2020

Successor Features Combine Elements of Model-Free and Model-based Reinforcement Learning

A key question in reinforcement learning is how an intelligent agent can generalize knowledge across different inputs. By generalizing across different inputs, information learned for one input can be immediately reused for improving predictions for another input. Reusing information allows an agent to compute an optimal decision-making strategy using less data. State representation is a key element of the generalization process, compressing a high-dimensional input space into a low-dimensional latent state space. This article analyzes properties of different latent state spaces, leading to new connections between model-based and model-free reinforcement learning. Successor features, which predict frequencies of future observations, form a link between model-based and model-free learning: Learning to predict future expected reward outcomes, a key characteristic of model-based agents, is equivalent to learning successor features. Learning successor features is a form of temporal difference learning and is equivalent to learning to predict a single policy's utility, which is a characteristic of model-free agents. Drawing on the connection between model-based reinforcement learning and successor features, we demonstrate that representations that are predictive of future reward outcomes generalize across variations in both transitions and rewards. This result extends previous work on successor features, which is constrained to fixed transitions and assumes re-learning of the transferred state representation.

cs.LG↗

arXiv2020

Mitigating Planner Overfitting in Model-Based Reinforcement Learning

An agent with an inaccurate model of its environment faces a difficult choice: it can ignore the errors in its model and act in the real world in whatever way it determines is optimal with respect to its model. Alternatively, it can take a more conservative stance and eschew its model in favor of optimizing its behavior solely via real-world interaction. This latter approach can be exceedingly slow to learn from experience, while the former can lead to "planner overfitting" - aspects of the agent's behavior are optimized to exploit errors in its model. This paper explores an intermediate position in which the planner seeks to avoid overfitting through a kind of regularization of the plans it considers. We present three different approaches that demonstrably mitigate planner overfitting in reinforcement-learning environments.

cs.LG↗

arXiv2020

The Efficiency of Human Cognition Reflects Planned Information Processing

Planning is useful. It lets people take actions that have desirable long-term consequences. But, planning is hard. It requires thinking about consequences, which consumes limited computational and cognitive resources. Thus, people should plan their actions, but they should also be smart about how they deploy resources used for planning their actions. Put another way, people should also "plan their plans". Here, we formulate this aspect of planning as a meta-reasoning problem and formalize it in terms of a recursive Bellman objective that incorporates both task rewards and information-theoretic planning costs. Our account makes quantitative predictions about how people should plan and meta-plan as a function of the overall structure of a task, which we test in two experiments with human participants. We find that people's reaction times reflect a planned use of information processing, consistent with our account. This formulation of planning to plan provides new insight into the function of hierarchical planning, state abstraction, and cognitive control in both humans and machines.

cs.AI↗

arXiv2020

Learning State Abstractions for Transfer in Continuous Control

Can simple algorithms with a good representation solve challenging reinforcement learning problems? In this work, we answer this question in the affirmative, where we take "simple learning algorithm" to be tabular Q-Learning, the "good representations" to be a learned state abstraction, and "challenging problems" to be continuous control tasks. Our main contribution is a learning algorithm that abstracts a continuous state-space into a discrete one. We transfer this learned representation to unseen problems to enable effective learning. We provide theory showing that learned abstractions maintain a bounded value loss, and we report experiments showing that the abstractions empower tabular Q-Learning to learn efficiently in unseen tasks.

cs.LG↗

arXiv2019

Individual predictions matter: Assessing the effect of data ordering in training fine-tuned CNNs for medical imaging

We reproduced the results of CheXNet with fixed hyperparameters and 50 different random seeds to identify 14 finding in chest radiographs (x-rays). Because CheXNet fine-tunes a pre-trained DenseNet, the random seed affects the ordering of the batches of training data but not the initialized model weights. We found substantial variability in predictions for the same radiograph across model runs (mean ln[(maximum probability)/(minimum probability)] 2.45, coefficient of variation 0.543). This individual radiograph-level variability was not fully reflected in the variability of AUC on a large test set. Averaging predictions from 10 models reduced variability by nearly 70% (mean coefficient of variation from 0.543 to 0.169, t-test 15.96, p-value < 0.0001). We encourage researchers to be aware of the potential variability of CNNs and ensemble predictions from multiple models to minimize the effect this variability may have on the care of individual patients when these models are deployed clinically.

cs.CV↗

arXiv2019

Stackelberg Punishment and Bully-Proofing Autonomous Vehicles

Mutually beneficial behavior in repeated games can be enforced via the threat of punishment, as enshrined in game theory's well-known "folk theorem." There is a cost, however, to a player for generating these disincentives. In this work, we seek to minimize this cost by computing a "Stackelberg punishment," in which the player selects a behavior that sufficiently punishes the other player while maximizing its own score under the assumption that the other player will adopt a best response. This idea generalizes the concept of a Stackelberg equilibrium. Known efficient algorithms for computing a Stackelberg equilibrium can be adapted to efficiently produce a Stackelberg punishment. We demonstrate an application of this idea in an experiment involving a virtual autonomous vehicle and human participants. We find that a self-driving car with a Stackelberg punishment policy discourages human drivers from bullying in a driving scenario requiring social negotiation.

cs.HC↗

arXiv2019

Interactive Learning of Environment Dynamics for Sequential Tasks

In order for robots and other artificial agents to efficiently learn to perform useful tasks defined by an end user, they must understand not only the goals of those tasks, but also the structure and dynamics of that user's environment. While existing work has looked at how the goals of a task can be inferred from a human teacher, the agent is often left to learn about the environment on its own. To address this limitation, we develop an algorithm, Behavior Aware Modeling (BAM), which incorporates a teacher's knowledge into a model of the transition dynamics of an agent's environment. We evaluate BAM both in simulation and with real human teachers, learning from a combination of task demonstrations and evaluative feedback, and show that it can outperform approaches which do not explicitly consider this source of dynamics knowledge.

cs.AI↗

arXiv2019

Deep Reinforcement Learning from Policy-Dependent Human Feedback

To widen their accessibility and increase their utility, intelligent agents must be able to learn complex behaviors as specified by (non-expert) human users. Moreover, they will need to learn these behaviors within a reasonable amount of time while efficiently leveraging the sparse feedback a human trainer is capable of providing. Recent work has shown that human feedback can be characterized as a critique of an agent's current behavior rather than as an alternative reward signal to be maximized, culminating in the COnvergent Actor-Critic by Humans (COACH) algorithm for making direct policy updates based on human feedback. Our work builds on COACH, moving to a setting where the agent's policy is represented by a deep neural network. We employ a series of modifications on top of the original COACH algorithm that are critical for successfully learning behaviors from high-dimensional observations, while also satisfying the constraint of obtaining reduced sample complexity. We demonstrate the effectiveness of our Deep COACH algorithm in the rich 3D world of Minecraft with an agent that learns to complete tasks by mapping from raw pixels to actions using only real-time human feedback in 10-15 minutes of interaction.

cs.LG↗

arXiv2019

Theory of Minds: Understanding Behavior in Groups Through Inverse Planning

Human social behavior is structured by relationships. We form teams, groups, tribes, and alliances at all scales of human life. These structures guide multi-agent cooperation and competition, but when we observe others these underlying relationships are typically unobservable and hence must be inferred. Humans make these inferences intuitively and flexibly, often making rapid generalizations about the latent relationships that underlie behavior from just sparse and noisy observations. Rapid and accurate inferences are important for determining who to cooperate with, who to compete with, and how to cooperate in order to compete. Towards the goal of building machine-learning algorithms with human-like social intelligence, we develop a generative model of multi-agent action understanding based on a novel representation for these latent relationships called Composable Team Hierarchies (CTH). This representation is grounded in the formalism of stochastic games and multi-agent reinforcement learning. We use CTH as a target for Bayesian inference yielding a new algorithm for understanding behavior in groups that can both infer hidden relationships as well as predict future actions for multiple agents interacting together. Our algorithm rapidly recovers an underlying causal model of how agents relate in spatial stochastic games from just a few observations. The patterns of inference made by this algorithm closely correspond with human judgments and the algorithm makes the same rapid generalizations that people do.

cs.AI↗

arXiv2018

Towards a Simple Approach to Multi-step Model-based Reinforcement Learning

When environmental interaction is expensive, model-based reinforcement learning offers a solution by planning ahead and avoiding costly mistakes. Model-based agents typically learn a single-step transition model. In this paper, we propose a multi-step model that predicts the outcome of an action sequence with variable length. We show that this model is easy to learn, and that the model can make policy-conditional predictions. We report preliminary results that show a clear advantage for the multi-step model compared to its one-step counterpart.

cs.LG↗

arXiv2018

Lipschitz Continuity in Model-based Reinforcement Learning

We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the Wasserstein metric. We go on to prove an error bound for the value-function estimate arising from Lipschitz models and show that the estimated value function is itself Lipschitz. We conclude with empirical results that show the benefits of controlling the Lipschitz constant of neural-network models.

cs.LG↗

arXiv2018

Equivalence Between Wasserstein and Value-Aware Loss for Model-based Reinforcement Learning

Learning a generative model is a key component of model-based reinforcement learning. Though learning a good model in the tabular setting is a simple task, learning a useful model in the approximate setting is challenging. In this context, an important question is the loss function used for model learning as varying the loss function can have a remarkable impact on effectiveness of planning. Recently Farahmand et al. (2017) proposed a value-aware model learning (VAML) objective that captures the structure of value function during model learning. Using tools from Asadi et al. (2018), we show that minimizing the VAML objective is in fact equivalent to minimizing the Wasserstein metric. This equivalence improves our understanding of value-aware models, and also creates a theoretical foundation for applications of Wasserstein in model-based reinforcement~learning.

cs.LG↗

arXiv2018

Transfer with Model Features in Reinforcement Learning

A key question in Reinforcement Learning is which representation an agent can learn to efficiently reuse knowledge between different tasks. Recently the Successor Representation was shown to have empirical benefits for transferring knowledge between tasks with shared transition dynamics. This paper presents Model Features: a feature representation that clusters behaviourally equivalent states and that is equivalent to a Model-Reduction. Further, we present a Successor Feature model which shows that learning Successor Features is equivalent to learning a Model-Reduction. A novel optimization objective is developed and we provide bounds showing that minimizing this objective results in an increasingly improved approximation of a Model-Reduction. Further, we provide transfer experiments on randomly generated MDPs which vary in their transition and reward functions but approximately preserve behavioural equivalence between states. These results demonstrate that Model Features are suitable for transfer between tasks with varying transition and reward functions.

cs.LG↗

arXiv2017

Modeling Latent Attention Within Neural Networks

Deep neural networks are able to solve tasks across a variety of domains and modalities of data. Despite many empirical successes, we lack the ability to clearly understand and interpret the learned internal mechanisms that contribute to such effective behaviors or, more critically, failure modes. In this work, we present a general method for visualizing an arbitrary neural network's inner mechanisms and their power and limitations. Our dataset-centric method produces visualizations of how a trained network attends to components of its inputs. The computed "attention masks" support improved interpretability by highlighting which input attributes are critical in determining output. We demonstrate the effectiveness of our framework on a variety of deep neural network architectures in domains from computer vision, natural language processing, and reinforcement learning. The primary contribution of our approach is an interpretable visualization of attention that provides unique insights into the network's underlying decision-making process irrespective of the data modality.

cs.AI↗

arXiv2017

Learning Approximate Stochastic Transition Models

We examine the problem of learning mappings from state to state, suitable for use in a model-based reinforcement-learning setting, that simultaneously generalize to novel states and can capture stochastic transitions. We show that currently popular generative adversarial networks struggle to learn these stochastic transition models but a modification to their loss functions results in a powerful learning algorithm for this class of problems.

cs.LG↗

arXiv2017

Summable Reparameterizations of Wasserstein Critics in the One-Dimensional Setting

Generative adversarial networks (GANs) are an exciting alternative to algorithms for solving density estimation problems---using data to assess how likely samples are to be drawn from the same distribution. Instead of explicitly computing these probabilities, GANs learn a generator that can match the given probabilistic source. This paper looks particularly at this matching capability in the context of problems with one-dimensional outputs. We identify a class of function decompositions with properties that make them well suited to the critic role in a leading approach to GANs known as Wasserstein GANs. We show that Taylor and Fourier series decompositions belong to our class, provide examples of these critics outperforming standard GAN approaches, and suggest how they can be scaled to higher dimensional problems in the future.

cs.LG↗