Jacob Adamczyk

Jacob Adamczyk, Argenis Arriojas, Stas Tiomkin et al.

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.

Jacob Adamczyk, Volodymyr Makarenko, Argenis Arriojas et al.

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.

Jacob Adamczyk, Stas Tiomkin, Rahul Kulkarni

An agent's ability to leverage past experience is critical for efficiently solving new tasks. Approximate solutions for new tasks can be obtained from previously derived value functions, as demonstrated by research on transfer learning, curriculum learning, and compositionality. However, prior work has primarily focused on using value functions to obtain zero-shot approximations for solutions to a new task. In this work, we show how an arbitrary approximation for the value function can be used to derive double-sided bounds on the optimal value function of interest. We further extend the framework with error analysis for continuous state and action spaces. The derived results lead to new approaches for clipping during training which we validate numerically in simple domains.

Jacob Adamczyk, Volodymyr Makarenko, Stas Tiomkin et al.

The average-reward formulation of reinforcement learning (RL) has drawn increased interest in recent years for its ability to solve temporally-extended problems without relying on discounting. Meanwhile, in the discounted setting, algorithms with entropy regularization have been developed, leading to improvements over deterministic methods. Despite the distinct benefits of these approaches, deep RL algorithms for the entropy-regularized average-reward objective have not been developed. While policy-gradient based approaches have recently been presented for the average-reward literature, the corresponding actor-critic framework remains less explored. In this paper, we introduce an average-reward soft actor-critic algorithm to address these gaps in the field. We validate our method by comparing with existing average-reward algorithms on standard RL benchmarks, achieving superior performance for the average-reward criterion.

Jacob Adamczyk, Juan Sebastian Rojas, Rahul V. Kulkarni

Connections between statistical mechanics and machine learning have repeatedly proven fruitful, providing insight into optimization, generalization, and representation learning. In this work, we follow this tradition by leveraging results from non-equilibrium thermodynamics to formalize curriculum learning in reinforcement learning (RL). In particular, we propose a geometric framework for RL by interpreting reward parameters as coordinates on a task manifold. We show that, by minimizing the excess thermodynamic work, optimal curricula correspond to geodesics in this task space. As an application of this framework, we provide an algorithm, "MEW" (Minimum Excess Work), to derive a principled schedule for temperature annealing in maximum-entropy RL.

Jacob Adamczyk, Adam Kamoski, Rahul V. Kulkarni

Efficient exploration remains a central challenge in reinforcement learning, serving as a useful pretraining objective for data collection, particularly when an external reward function is unavailable. A principled formulation of the exploration problem is to find policies that maximize the entropy of their induced steady-state visitation distribution, thereby encouraging uniform long-run coverage of the state space. Many existing exploration approaches require estimating state visitation frequencies through repeated on-policy rollouts, which can be computationally expensive. In this work, we instead consider an intrinsic average-reward formulation in which the reward is derived from the visitation distribution itself, so that the optimal policy maximizes steady-state entropy. An entropy-regularized version of this objective admits a spectral characterization: the relevant stationary distributions can be computed from the dominant eigenvectors of a problem-dependent transition matrix. This insight leads to a novel algorithm for solving the maximum entropy exploration problem, EVE (EigenVector-based Exploration), which avoids explicit rollouts and distribution estimation, instead computing the solution through iterative updates, similar to a value-based approach. To address the original unregularized objective, we employ a posterior-policy iteration (PPI) approach, which monotonically improves the entropy and converges in value. We prove convergence of EVE under standard assumptions and demonstrate empirically that it efficiently produces policies with high steady-state entropy, achieving competitive exploration performance relative to rollout-based baselines in deterministic grid-world environments.

Jacob Adamczyk

Exploration remains a fundamental challenge in reinforcement learning (RL), particularly in environments with sparse or adversarial reward structures. In this work, we study how the architecture of deep neural policies implicitly shapes exploration before training. We theoretically and empirically demonstrate strategies for generating ballistic or diffusive trajectories from untrained policies in a toy model. Using the theory of infinite-width networks and a continuous-time limit, we show that untrained policies return correlated actions and result in non-trivial state-visitation distributions. We discuss the distributions of the corresponding trajectories for a standard architecture, revealing insights into inductive biases for tackling exploration. Our results establish a theoretical and experimental framework for using policy initialization as a design tool to understand exploration behavior in early training.

Jacob Adamczyk

In reinforcement learning, the value function is typically trained to solve the Bellman equation, which connects the current value to future values. This temporal dependency hints that the value function may contain implicit information about the environment's transition dynamics. By rearranging the Bellman equation, we show that a converged value function encodes a model of the underlying dynamics of the environment. We build on this insight to propose a simple method for inferring dynamics models directly from the value function, potentially mitigating the need for explicit model learning. Furthermore, we explore the challenges of next-state identifiability, discussing conditions under which the inferred dynamics model is well-defined. Our work provides a theoretical foundation for leveraging value functions in dynamics modeling and opens a new avenue for bridging model-free and model-based reinforcement learning.

Jacob Adamczyk, Volodymyr Makarenko, Stas Tiomkin et al.

In reinforcement learning, two objective functions have been developed extensively in the literature: discounted and averaged rewards. The generalization to an entropy-regularized setting has led to improved robustness and exploration for both of these objectives. Recently, the entropy-regularized average-reward problem was addressed using tools from large deviation theory in the tabular setting. This method has the advantage of linearity, providing access to both the optimal policy and average reward-rate through properties of a single matrix. In this paper, we extend that framework to more general settings by developing approaches based on function approximation by neural networks. This formulation reveals new theoretical insights into the relationship between different objectives used in RL. Additionally, we combine our algorithm with a posterior policy iteration scheme, showing how our approach can also solve the average-reward RL problem without entropy-regularization. Using classic control benchmarks, we experimentally find that our method compares favorably with other algorithms in terms of stability and rate of convergence.

Jacob Adamczyk, Volodymyr Makarenko, Stas Tiomkin et al.

In reinforcement learning, especially in sparse-reward domains, many environment steps are required to observe reward information. In order to increase the frequency of such observations, "potential-based reward shaping" (PBRS) has been proposed as a method of providing a more dense reward signal while leaving the optimal policy invariant. However, the required "potential function" must be carefully designed with task-dependent knowledge to not deter training performance. In this work, we propose a "bootstrapped" method of reward shaping, termed BSRS, in which the agent's current estimate of the state-value function acts as the potential function for PBRS. We provide convergence proofs for the tabular setting, give insights into training dynamics for deep RL, and show that the proposed method improves training speed in the Atari suite.

Josiah C. Kratz, Jacob Adamczyk

Many organisms and cell types, from bacteria to cancer cells, exhibit a remarkable ability to adapt to fluctuating environments. Additionally, cells can leverage a memory of past environments to better survive previously-encountered stressors. From a control perspective, this adaptability poses significant challenges in driving cell populations toward extinction, and thus poses an open question with great clinical significance. In this work, we focus on drug dosing in cell populations exhibiting phenotypic plasticity. For specific dynamical models switching between resistant and susceptible states, exact solutions are known. However, when the underlying system parameters are unknown, and for complex memory-based systems, obtaining the optimal solution is currently intractable. To address this challenge, we apply reinforcement learning (RL) to identify informed dosing strategies to control cell populations evolving under novel non-Markovian dynamics. We find that model-free deep RL is able to recover exact solutions and control cell populations even in the presence of long-range temporal dynamics. To further test our approach in more realistic settings, we demonstrate robust RL-based control strategies in environments with measurement noise and dynamic memory strength.

Jacob Adamczyk, Volodymyr Makarenko, Stas Tiomkin et al.

An agent's ability to leverage past experience is critical for efficiently solving new tasks. Prior work has focused on using value function estimates to obtain zero-shot approximations for solutions to a new task. In soft Q-learning, we show how any value function estimate can also be used to derive double-sided bounds on the optimal value function. The derived bounds lead to new approaches for boosting training performance which we validate experimentally. Notably, we find that the proposed framework suggests an alternative method for updating the Q-function, leading to boosted performance.

Argenis Arriojas, Jacob Adamczyk, Stas Tiomkin et al.

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.

Jacob Adamczyk

This report discusses the application of neural networks (NNs) as small segments of the brain. The networks representing the biological connectome are altered both spatially and temporally. The degradation techniques applied here are "weight degradation", "weight scrambling", and variable activation function. These methods aim to shine light on the study of neurodegenerative diseases such as Alzheimer's, Huntington's and Parkinson's disease as well as strokes and brain tumors disrupting the flow of information in the brain's network. Fundamental insights to memory loss and generalized learning dysfunction are gained by monitoring the network's error function during network degradation. The biological significance of each facet is also discussed.