SuPLE: Robot Learning with Lyapunov Rewards

The reward function is an essential component in robot learning. Reward directly affects the sample and computational complexity of learning, and the quality of a solution. The design of informative rewards requires domain knowledge, which is not always available. We use the properties of the dynamics to produce system-appropriate reward without adding external assumptions. Specifically, we explore an approach to utilize the Lyapunov exponents of the system dynamics to generate a system-immanent reward. We demonstrate that the `Sum of the Positive Lyapunov Exponents' (SuPLE) is a strong candidate for the design of such a reward. We develop a computational framework for the derivation of this reward, and demonstrate its effectiveness on classical benchmarks for sample-based stabilization of various dynamical systems. It eliminates the need to start the training trajectories at arbitrary states, also known as auxiliary exploration. While the latter is a common practice in simulated robot learning, it is unpractical to consider to use it in real robotic systems, since they typically start from natural rest states such as a pendulum at the bottom, a robot on the ground, etc. and can not be easily initialized at arbitrary states. Comparing the performance of SuPLE to commonly-used reward functions, we observe that the latter fail to find a solution without auxiliary exploration, even for the task of swinging up the double pendulum and keeping it stable at the upright position, a prototypical scenario for multi-linked robots. SuPLE-induced rewards for robot learning offer a novel route for effective robot learning in typical as opposed to highly specialized or fine-tuned scenarios. Our code is publicly available for reproducibility and further research.

Boosting Soft Q-Learning by Bounding

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.

Learning telic-controllable state representations

Computational accounts of purposeful behavior consist of descriptive and normative aspects. The former enable agents to ascertain the current (or future) state of affairs in the world and the latter to evaluate the desirability, or lack thereof, of these states with respect to the agent's goals. In Reinforcement Learning, the normative aspect (reward and value functions) is assumed to depend on a pre-defined and fixed descriptive one (state representation). Alternatively, these two aspects may emerge interdependently: goals can be, and indeed often are, expressed in terms of state representation features, but they may also serve to shape state representations themselves. Here, we illustrate a novel theoretical framing of state representation learning in bounded agents, coupling descriptive and normative aspects via the notion of goal-directed, or telic, states. We define a new controllability property of telic state representations to characterize the tradeoff between their granularity and the policy complexity capacity required to reach all telic states. We propose an algorithm for learning controllable state representations and demonstrate it using a simple navigation task with changing goals. Our framework highlights the crucial role of deliberate ignorance - knowing what to ignore - for learning state representations that are both goal-flexible and simple. More broadly, our work provides a concrete step towards a unified theoretical view of natural and artificial learning through the lens of goals.

Multi-Resolution Diffusion for Privacy-Sensitive Recommender Systems

While recommender systems have become an integral component of the Web experience, their heavy reliance on user data raises privacy and security concerns. Substituting user data with synthetic data can address these concerns, but accurately replicating these real-world datasets has been a notoriously challenging problem. Recent advancements in generative AI have demonstrated the impressive capabilities of diffusion models in generating realistic data across various domains. In this work we introduce a Score-based Diffusion Recommendation Module (SDRM), which captures the intricate patterns of real-world datasets required for training highly accurate recommender systems. SDRM allows for the generation of synthetic data that can replace existing datasets to preserve user privacy, or augment existing datasets to address excessive data sparsity. Our method outperforms competing baselines such as generative adversarial networks, variational autoencoders, and recently proposed diffusion models in synthesizing various datasets to replace or augment the original data by an average improvement of 4.30% in Recall@$k$ and 4.65% in NDCG@$k$.

Dimensionality Reduction of Dynamics on Lie Manifolds via Structure-Aware Canonical Correlation Analysis

Incorporating prior knowledge into a data-driven modeling problem can drastically improve performance, reliability, and generalization outside of the training sample. The stronger the structural properties, the more effective these improvements become. Manifolds are a powerful nonlinear generalization of Euclidean space for modeling finite dimensions. Structural impositions in constrained systems increase when applying group structure, converting them into Lie manifolds. The range of their applications is very wide and includes the important case of robotic tasks. Canonical Correlation Analysis (CCA) can construct a hierarchical sequence of maximal correlations of up to two paired data sets in these Euclidean spaces. We present a method to generalize this concept to Lie Manifolds and demonstrate its efficacy through the substantial improvements it achieves in making structure-consistent predictions about changes in the state of a robotic hand.

Controllability-Constrained Deep Network Models for Enhanced Control of Dynamical Systems

Control of a dynamical system without the knowledge of dynamics is an important and challenging task. Modern machine learning approaches, such as deep neural networks (DNNs), allow for the estimation of a dynamics model from control inputs and corresponding state observation outputs. Such data-driven models are often utilized for the derivation of model-based controllers. However, in general, there are no guarantees that a model represented by DNNs will be controllable according to the formal control-theoretical meaning of controllability, which is crucial for the design of effective controllers. This often precludes the use of DNN-estimated models in applications, where formal controllability guarantees are required. In this proof-of-the-concept work, we propose a control-theoretical method that explicitly enhances models estimated from data with controllability. That is achieved by augmenting the model estimation objective with a controllability constraint, which penalizes models with a low degree of controllability. As a result, the models estimated with the proposed controllability constraint allow for the derivation of more efficient controllers, they are interpretable by the control-theoretical quantities and have a lower long-term prediction error. The proposed method provides new insights on the connection between the DNN-based estimation of unknown dynamics and the control-theoretical guarantees of the solution properties. We demonstrate the superiority of the proposed method in two standard classical control systems with state observation given by low resolution high-dimensional images.

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.

Compositionality and Bounds for Optimal Value Functions in Reinforcement Learning

An agent's ability to reuse solutions to previously solved problems is critical for learning new tasks efficiently. Recent research using composition of value functions in reinforcement learning has shown that agents can utilize solutions of primitive tasks to obtain solutions for exponentially many new tasks. However, previous work has relied on restrictive assumptions on the dynamics, the method of composition, and the structure of reward functions. Here we consider the case of general composition functions without any restrictions on the structure of reward functions, applicable to both deterministic and stochastic dynamics. For this general setup, we provide bounds on the corresponding optimal value functions and characterize the value of corresponding policies. The theoretical results derived lead to improvements in training for both entropy-regularized and standard reinforcement learning, which we validate with numerical simulations.

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.

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.