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.

Towards Information Theory-Based Discovery of Equivariances

The presence of symmetries imposes a stringent set of constraints on a system. This constrained structure allows intelligent agents interacting with such a system to drastically improve the efficiency of learning and generalization, through the internalisation of the system's symmetries into their information-processing. In parallel, principled models of complexity-constrained learning and behaviour make increasing use of information-theoretic methods. Here, we wish to marry these two perspectives and understand whether and in which form the information-theoretic lens can "see" the effect of symmetries of a system. For this purpose, we propose a novel variant of the Information Bottleneck principle, which has served as a productive basis for many principled studies of learning and information-constrained adaptive behaviour. We show (in the discrete case) that our approach formalises a certain duality between symmetry and information parsimony: namely, channel equivariances can be characterised by the optimal mutual information-preserving joint compression of the channel's input and output. This information-theoretic treatment furthermore suggests a principled notion of "soft" equivariance, whose "coarseness" is measured by the amount of input-output mutual information preserved by the corresponding optimal compression. This new notion offers a bridge between the field of bounded rationality and the study of symmetries in neural representations. The framework may also allow (exact and soft) equivariances to be automatically discovered.

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.

A space of goals: the cognitive geometry of informationally bounded agents

Traditionally, Euclidean geometry is treated by scientists as a priori and objective. However, when we take the position of an agent, the problem of selecting a best route should also factor in the abilities of the agent, its embodiment and particularly its cognitive effort. In this paper we consider geometry in terms of travel between states within a world by incorporating information processing costs with the appropriate spatial distances. This induces a geometry that increasingly differs from the original geometry of the given world, as information costs become increasingly important. We visualize this \textit{"cognitive geometry"} by projecting it onto 2- and 3-dimensional spaces showing distinct distortions reflecting the emergence of epistemic and information-saving strategies as well as pivot states. The analogies between traditional cost-based geometries and those induced by additional informational costs invite a generalization of the traditional notion of geodesics as cheapest routes towards the notion of \textit{infodesics}. Crucially, the concept of infodesics approximates the usual geometric property that, travelling from a start to a goal along a geodesic, not only the goal, but all intermediate points are equally visited at optimal cost from the start.

Causal blankets: Theory and algorithmic framework

We introduce a novel framework to identify perception-action loops (PALOs) directly from data based on the principles of computational mechanics. Our approach is based on the notion of causal blanket, which captures sensory and active variables as dynamical sufficient statistics -- i.e. as the "differences that make a difference." Moreover, our theory provides a broadly applicable procedure to construct PALOs that requires neither a steady-state nor Markovian dynamics. Using our theory, we show that every bipartite stochastic process has a causal blanket, but the extent to which this leads to an effective PALO formulation varies depending on the integrated information of the bipartition.

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.

Human Perception of Intrinsically Motivated Autonomy in Human-Robot Interaction

A challenge in using fully autonomous robots in human-robot interaction (HRI) is to design behavior that is engaging enough to encourage voluntary, long-term interaction, yet robust to the perturbations induced by human interaction. Here we evaluate if an intrinsically motivated, physical robot can address this challenge. We use predictive information maximization as an intrinsic motivation, as simulated experiments showed that this leads to playful, exploratory behavior that is robust to changes in the robot's morphology and environment. To the authors' knowledge there are no previous HRI studies that evaluate the effect of intrinsically motivated behavior in robots on the human perception of those robots. We present a game-like study design, which allows us to focus on the interplay between the robot and the human participant. In contrast to a study design where participants order or control a robot to do a specific task, the robot and the human participants in our study design explore their behaviors without knowledge about any specific goals. We conducted a within-subjects study (N=24) were participants interacted with a fully autonomous Sphero BB8 robot with different behavioral regimes: one realizing an adaptive, intrinsically motivated behavior and the other being reactive, but not adaptive. A quantitative analysis of post-interaction questionnaires showed a significantly higher perception (r=.555, p=.007) of the dimension "Warmth" compared to the baseline behavior. Warmth is considered a primary dimension for social attitude formation in human cognition. A human perceived as warm (i.e. friendly and trustworthy) experiences more positive social interactions. If future work demonstrates that this transfers to human-robot social cognition, then the generic methods presented here could be used to imbue robots with behavior leading to positive perception by humans.