arXiv subjects

Stas Tiomkin

Publications and source records attributed to Stas Tiomkin.

32 records · Page 2Linked to original sources

arXiv2023

Bounding the Optimal Value Function in Compositional Reinforcement Learning

In the field of reinforcement learning (RL), agents are often tasked with solving a variety of problems differing only in their reward functions. In order to quickly obtain solutions to unseen problems with new reward functions, a popular approach involves functional composition of previously solved tasks. However, previous work using such functional composition has primarily focused on specific instances of composition functions whose limiting assumptions allow for exact zero-shot composition. Our work unifies these examples and provides a more general framework for compositionality in both standard and entropy-regularized RL. We find that, for a broad class of functions, the optimal solution for the composite task of interest can be related to the known primitive task solutions. Specifically, we present double-sided inequalities relating the optimal composite value function to the value functions for the primitive tasks. We also show that the regret of using a zero-shot policy can be bounded for this class of functions. The derived bounds can be used to develop clipping approaches for reducing uncertainty during training, allowing agents to quickly adapt to new tasks.

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arXiv2023

Entropy Regularized Reinforcement Learning Using Large Deviation Theory

Reinforcement learning (RL) is an important field of research in machine learning that is increasingly being applied to complex optimization problems in physics. In parallel, concepts from physics have contributed to important advances in RL with developments such as entropy-regularized RL. While these developments have led to advances in both fields, obtaining analytical solutions for optimization in entropy-regularized RL is currently an open problem. In this paper, we establish a mapping between entropy-regularized RL and research in non-equilibrium statistical mechanics focusing on Markovian processes conditioned on rare events. In the long-time limit, we apply approaches from large deviation theory to derive exact analytical results for the optimal policy and optimal dynamics in Markov Decision Process (MDP) models of reinforcement learning. The results obtained lead to a novel analytical and computational framework for entropy-regularized RL which is validated by simulations. The mapping established in this work connects current research in reinforcement learning and non-equilibrium statistical mechanics, thereby opening new avenues for the application of analytical and computational approaches from one field to cutting-edge problems in the other.

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arXiv2022

Utilizing Prior Solutions for Reward Shaping and Composition in Entropy-Regularized Reinforcement Learning

In reinforcement learning (RL), the ability to utilize prior knowledge from previously solved tasks can allow agents to quickly solve new problems. In some cases, these new problems may be approximately solved by composing the solutions of previously solved primitive tasks (task composition). Otherwise, prior knowledge can be used to adjust the reward function for a new problem, in a way that leaves the optimal policy unchanged but enables quicker learning (reward shaping). In this work, we develop a general framework for reward shaping and task composition in entropy-regularized RL. To do so, we derive an exact relation connecting the optimal soft value functions for two entropy-regularized RL problems with different reward functions and dynamics. We show how the derived relation leads to a general result for reward shaping in entropy-regularized RL. We then generalize this approach to derive an exact relation connecting optimal value functions for the composition of multiple tasks in entropy-regularized RL. We validate these theoretical contributions with experiments showing that reward shaping and task composition lead to faster learning in various settings.

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arXiv2022

Intrinsic Motivation in Dynamical Control Systems

Biological systems often choose actions without an explicit reward signal, a phenomenon known as intrinsic motivation. The computational principles underlying this behavior remain poorly understood. In this study, we investigate an information-theoretic approach to intrinsic motivation, based on maximizing an agent's empowerment (the mutual information between its past actions and future states). We show that this approach generalizes previous attempts to formalize intrinsic motivation, and we provide a computationally efficient algorithm for computing the necessary quantities. We test our approach on several benchmark control problems, and we explain its success in guiding intrinsically motivated behaviors by relating our information-theoretic control function to fundamental properties of the dynamical system representing the combined agent-environment system. This opens the door for designing practical artificial, intrinsically motivated controllers and for linking animal behaviors to their dynamical properties.

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arXiv2022

Multi-Objective Policy Gradients with Topological Constraints

Multi-objective optimization models that encode ordered sequential constraints provide a solution to model various challenging problems including encoding preferences, modeling a curriculum, and enforcing measures of safety. A recently developed theory of topological Markov decision processes (TMDPs) captures this range of problems for the case of discrete states and actions. In this work, we extend TMDPs towards continuous spaces and unknown transition dynamics by formulating, proving, and implementing the policy gradient theorem for TMDPs. This theoretical result enables the creation of TMDP learning algorithms that use function approximators, and can generalize existing deep reinforcement learning (DRL) approaches. Specifically, we present a new algorithm for a policy gradient in TMDPs by a simple extension of the proximal policy optimization (PPO) algorithm. We demonstrate this on a real-world multiple-objective navigation problem with an arbitrary ordering of objectives both in simulation and on a real robot.

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arXiv2021

Efficient Empowerment Estimation for Unsupervised Stabilization

Intrinsically motivated artificial agents learn advantageous behavior without externally-provided rewards. Previously, it was shown that maximizing mutual information between agent actuators and future states, known as the empowerment principle, enables unsupervised stabilization of dynamical systems at upright positions, which is a prototypical intrinsically motivated behavior for upright standing and walking. This follows from the coincidence between the objective of stabilization and the objective of empowerment. Unfortunately, sample-based estimation of this kind of mutual information is challenging. Recently, various variational lower bounds (VLBs) on empowerment have been proposed as solutions; however, they are often biased, unstable in training, and have high sample complexity. In this work, we propose an alternative solution based on a trainable representation of a dynamical system as a Gaussian channel, which allows us to efficiently calculate an unbiased estimator of empowerment by convex optimization. We demonstrate our solution for sample-based unsupervised stabilization on different dynamical control systems and show the advantages of our method by comparing it to the existing VLB approaches. Specifically, we show that our method has a lower sample complexity, is more stable in training, possesses the essential properties of the empowerment function, and allows estimation of empowerment from images. Consequently, our method opens a path to wider and easier adoption of empowerment for various applications.

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arXiv2021

GEM: Group Enhanced Model for Learning Dynamical Control Systems

Learning the dynamics of a physical system wherein an autonomous agent operates is an important task. Often these systems present apparent geometric structures. For instance, the trajectories of a robotic manipulator can be broken down into a collection of its transitional and rotational motions, fully characterized by the corresponding Lie groups and Lie algebras. In this work, we take advantage of these structures to build effective dynamical models that are amenable to sample-based learning. We hypothesize that learning the dynamics on a Lie algebra vector space is more effective than learning a direct state transition model. To verify this hypothesis, we introduce the Group Enhanced Model (GEM). GEMs significantly outperform conventional transition models on tasks of long-term prediction, planning, and model-based reinforcement learning across a diverse suite of standard continuous-control environments, including Walker, Hopper, Reacher, Half-Cheetah, Inverted Pendulums, Ant, and Humanoid. Furthermore, plugging GEM into existing state of the art systems enhances their performance, which we demonstrate on the PETS system. This work sheds light on a connection between learning of dynamics and Lie group properties, which opens doors for new research directions and practical applications along this direction. Our code is publicly available at: https://tinyurl.com/GEMMBRL.

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arXiv2021

AvE: Assistance via Empowerment

One difficulty in using artificial agents for human-assistive applications lies in the challenge of accurately assisting with a person's goal(s). Existing methods tend to rely on inferring the human's goal, which is challenging when there are many potential goals or when the set of candidate goals is difficult to identify. We propose a new paradigm for assistance by instead increasing the human's ability to control their environment, and formalize this approach by augmenting reinforcement learning with human empowerment. This task-agnostic objective preserves the person's autonomy and ability to achieve any eventual state. We test our approach against assistance based on goal inference, highlighting scenarios where our method overcomes failure modes stemming from goal ambiguity or misspecification. As existing methods for estimating empowerment in continuous domains are computationally hard, precluding its use in real time learned assistance, we also propose an efficient empowerment-inspired proxy metric. Using this, we are able to successfully demonstrate our method in a shared autonomy user study for a challenging simulated teleoperation task with human-in-the-loop training.

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arXiv2020

Predictive Coding for Boosting Deep Reinforcement Learning with Sparse Rewards

While recent progress in deep reinforcement learning has enabled robots to learn complex behaviors, tasks with long horizons and sparse rewards remain an ongoing challenge. In this work, we propose an effective reward shaping method through predictive coding to tackle sparse reward problems. By learning predictive representations offline and using these representations for reward shaping, we gain access to reward signals that understand the structure and dynamics of the environment. In particular, our method achieves better learning by providing reward signals that 1) understand environment dynamics 2) emphasize on features most useful for learning 3) resist noise in learned representations through reward accumulation. We demonstrate the usefulness of this approach in different domains ranging from robotic manipulation to navigation, and we show that reward signals produced through predictive coding are as effective for learning as hand-crafted rewards.

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arXiv2020

Dynamics Generalization via Information Bottleneck in Deep Reinforcement Learning

Despite the significant progress of deep reinforcement learning (RL) in solving sequential decision making problems, RL agents often overfit to training environments and struggle to adapt to new, unseen environments. This prevents robust applications of RL in real world situations, where system dynamics may deviate wildly from the training settings. In this work, our primary contribution is to propose an information theoretic regularization objective and an annealing-based optimization method to achieve better generalization ability in RL agents. We demonstrate the extreme generalization benefits of our approach in different domains ranging from maze navigation to robotic tasks; for the first time, we show that agents can generalize to test parameters more than 10 standard deviations away from the training parameter distribution. This work provides a principled way to improve generalization in RL by gradually removing information that is redundant for task-solving; it opens doors for the systematic study of generalization from training to extremely different testing settings, focusing on the established connections between information theory and machine learning.

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arXiv2020

Learning Efficient Representation for Intrinsic Motivation

Mutual Information between agent Actions and environment States (MIAS) quantifies the influence of agent on its environment. Recently, it was found that the maximization of MIAS can be used as an intrinsic motivation for artificial agents. In literature, the term empowerment is used to represent the maximum of MIAS at a certain state. While empowerment has been shown to solve a broad range of reinforcement learning problems, its calculation in arbitrary dynamics is a challenging problem because it relies on the estimation of mutual information. Existing approaches, which rely on sampling, are limited to low dimensional spaces, because high-confidence distribution-free lower bounds for mutual information require exponential number of samples. In this work, we develop a novel approach for the estimation of empowerment in unknown dynamics from visual observation only, without the need to sample for MIAS. The core idea is to represent the relation between action sequences and future states using a stochastic dynamic model in latent space with a specific form. This allows us to efficiently compute empowerment with the "Water-Filling" algorithm from information theory. We construct this embedding with deep neural networks trained on a sophisticated objective function. Our experimental results show that the designed embedding preserves information-theoretic properties of the original dynamics.

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arXiv2020

Preventing Imitation Learning with Adversarial Policy Ensembles

Imitation learning can reproduce policies by observing experts, which poses a problem regarding policy privacy. Policies, such as human, or policies on deployed robots, can all be cloned without consent from the owners. How can we protect against external observers cloning our proprietary policies? To answer this question we introduce a new reinforcement learning framework, where we train an ensemble of near-optimal policies, whose demonstrations are guaranteed to be useless for an external observer. We formulate this idea by a constrained optimization problem, where the objective is to improve proprietary policies, and at the same time deteriorate the virtual policy of an eventual external observer. We design a tractable algorithm to solve this new optimization problem by modifying the standard policy gradient algorithm. Our formulation can be interpreted in lenses of confidentiality and adversarial behaviour, which enables a broader perspective of this work. We demonstrate the existence of "non-clonable" ensembles, providing a solution to the above optimization problem, which is calculated by our modified policy gradient algorithm. To our knowledge, this is the first work regarding the protection of policies in Reinforcement Learning.

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arXiv2018

A Unified Bellman Equation for Causal Information and Value in Markov Decision Processes

The interaction between an artificial agent and its environment is bi-directional. The agent extracts relevant information from the environment, and affects the environment by its actions in return to accumulate high expected reward. Standard reinforcement learning (RL) deals with the expected reward maximization. However, there are always information-theoretic limitations that restrict the expected reward, which are not properly considered by the standard RL. In this work we consider RL objectives with information-theoretic limitations. For the first time we derive a Bellman-type recursive equa- tion for the causal information between the environment and the agent, which is combined plausibly with the Bellman recursion for the value function. The unified equitation serves to explore the typical behavior of artificial agents in an infinite time horizon.

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arXiv2017

Control Capacity of Partially Observable Dynamic Systems in Continuous Time

Stochastic dynamic control systems relate in a prob- abilistic fashion the space of control signals to the space of corresponding future states. Consequently, stochastic dynamic systems can be interpreted as an information channel between the control space and the state space. In this work we study this control-to-state informartion capacity of stochastic dynamic systems in continuous-time, when the states are observed only partially. The control-to-state capacity, known as empowerment, was shown in the past to be useful in solving various Artificial Intelligence & Control benchmarks, and was used to replace problem-specific utilities. The higher the value of empowerment is, the more optional future states an agent may reach by using its controls inside a given time horizon. The contribution of this work is that we derive an efficient solution for computing the control-to-state information capacity for a linear, partially-observed Gaussian dynamic control system in continuous time, and discover new relationships between control-theoretic and information-theoretic properties of dynamic systems. Particularly, using the derived method, we demonstrate that the capacity between the control signal and the system output does not grow without limits with the length of the control signal. This means that only the near-past window of the control signal contributes effectively to the control-to-state capacity, while most of the information beyond this window is irrelevant for the future state of the dynamic system. We show that empowerment depends on a time constant of a dynamic system.

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