A probabilistic interpretation of PID controllers using active inference

In the past few decades, probabilistic interpretations of brain functions have become widespread in cognitive science and neuroscience. The Bayesian brain hypothesis, predictive coding, the free energy principle and active inference are increasingly popular theories of cognitive functions that claim to unify understandings of life and cognition within general mathematical frameworks derived from information and control theory, statistical physics and machine learning. The connections between information and control theory have been discussed since the 1950’s by scientists like Shannon and Kalman and have recently risen to prominence in modern stochastic optimal control theory. However, the implications of the confluence of these two theoretical frameworks for the biological sciences have been slow to emerge. Here we argue that if the active inference proposal is to be taken as a general process theory for biological systems, we need to consider how existing control theoretical approaches to biological systems relate to it. In this work we will focus on PID (Proportional-Integral-Derivative) controllers, one of the most common types of regulators employed in engineering and more recently used to explain behaviour in biological systems, e.g. chemotaxis in bacteria and amoebae or robust adaptation in biochemical networks. Using active inference, we derive a probabilistic interpretation of PID controllers, showing how they can fit a more general theory of life and cognition under the principle of (variational) free energy minimisation under simple linear generative models.most common types of regulators employed in engineering and more recently used to explain behaviour in biological systems, e.g. chemotaxis in bacteria and amoebae or robust adaptation in biochemical networks. Using active inference, we derive a probabilistic interpretation of PID controllers, showing how they can fit a more general theory of life and cognition under the principle of (variational) free energy minimisation under simple linear generative models

PID control as a process of active inference with linear generative models

In the past few decades, probabilistic interpretations of brain functions have become widespread in cognitive science and neuroscience. In particular, the free energy principle and active inference are increasingly popular theories of cognitive functions that claim to offer a unified understanding of life and cognition within a general mathematical framework derived from information and control theory, and statistical mechanics. However, we argue that if the active inference proposal is to be taken as a general process theory for biological systems, it is necessary to understand how it relates to existing control theoretical approaches routinely used to study and explain biological systems. For example, recently, PID control has been shown to be implemented in simple molecular systems and is becoming a popular mechanistic explanation of behaviours such as chemotaxis in bacteria and amoebae, and robust adaptation in biochemical networks. In this work, we will show how PID controllers can fit a more general theory of life and cognition under the principle of (variational) free energy minimisation when using approximate linear generative models of the world. This more general interpretation provides also a new perspective on traditional problems of PID controllers such as parameter tuning as well as the need to balance performances and robustness conditions of a controller. Specifically, we then show how these problems can be understood in terms of the optimisation of the precisions (inverse variances) modulating different prediction errors in the free energy functional

A Bayesian perspective on classical control

The connections between optimal control and Bayesian inference have long been recognised, with the field of stochastic (optimal) control combining these frameworks for the solution of partially observable control problems. In particular, for the linear case with quadratic functions and Gaussian noise, stochastic control has shown remarkable results in different fields, including robotics, reinforcement learning and neuroscience, especially thanks to the established duality of estimation and control processes. Following this idea we recently introduced a formulation of PID control, one of the most popular methods from classical control, based on active inference, a theory with roots in variational Bayesian methods, and applications in the biological and neural sciences. In this work, we highlight the advantages of our previous formulation and introduce new and more general ways to tackle some existing problems in current controller design procedures. In particular, we consider 1) a gradient-based tuning rule for the parameters (or gains) of a PID controller, 2) an implementation of multiple degrees of freedom for independent responses to different types of signals (e.g., two-degree-of-freedom PID), and 3) a novel time-domain formalisation of the performance-robustness trade-off in terms of tunable constraints (i.e., priors in a Bayesian model) of a single cost functional, variational free energy.Comment: 8 pages, Accepted at IJCNN 202

Granular synthesis for display of time-varying probability densities

We present a method for displaying time-varying probabilistic information to users using an asynchronous granular synthesis technique. We extend the basic synthesis technique to include distribution over waveform source, spatial position, pitch and time inside waveforms. To enhance the synthesis in interactive contexts, we "quicken" the display by integrating predictions of user behaviour into the sonification. This includes summing the derivatives of the distribution during exploration of static densities, and using Monte-Carlo sampling to predict future user states in nonlinear dynamic systems. These techniques can be used to improve user performance in continuous control systems and in the interactive exploration of high dimensional spaces. This technique provides feedback from users potential goals, and their progress toward achieving them; modulating the feedback with quickening can help shape the users actions toward achieving these goals. We have applied these techniques to a simple nonlinear control problem as well as to the sonification of on-line probabilistic gesture recognition. We are applying these displays to mobile, gestural interfaces, where visual display is often impractical. The granular synthesis approach is theoretically elegant and easily applied in contexts where dynamic probabilistic displays are required

Active inference: building a new bridge between control theory and embodied cognitive science

The application of Bayesian techniques to the study and computational modelling of biological systems is one of the most remarkable advances in the natural and cognitive sciences over the last 50 years. More recently, it has been proposed that Bayesian frameworks are not only useful for building descriptive models of biological functions, but that living systems themselves can be seen as Bayesian (inference) machines. On this view, the statistical tools more traditionally used to account for data in biology, neuroscience and psychology, are now used to model the mechanisms underlying functions and properties of living systems as if the systems themselves were the ones“calculating”those probabilities following Bayesian inference schemes. The free energy principle (FEP) is a framework proposed in light of this paradigm shift, advocating the minimisation of variational free energy, a proxy for sensory surprisal, as a general computational principle for biological systems. More intuitively and under some simplifying assumptions,the minimisation of variational free energy reduces,for an agent,to the minimisation of prediction errors on sensory input. Initially proposed as a candidate unifying theory of brain functioning, the FEP was later extended to encompass hypotheses on the origins of life, and is nowadays discussed in the cognitive science community for its possible implications for theories of the mind. In particular,one of the most popular process theories derived from the FEP,active inference,describes a biologically plausible algorithmic implementation of this principle with several repercussions on our understanding of cognition. In this thesis, I will focus on the role of this process theory for action and perception. In active inference, the two of them are combined in a closed sensorimotor loopasco-dependent processes of minimisation of a single loss function,variational free energy, with respect to different sets of variables. Building on this, I will suggest that some of the core ideas of active inference are best seen in terms of enactive, embodied, extended and embedded (4E) theories, in contrast to the majority of the literature emphasising its apparent connections to more traditional, computational, accounts of the mind. In particular, I will develop this argument by focusing on some proposals central to 4E approaches: (a) the non-brain-centric nature of cognitive processes,(b)the lack of explicit representations of the world,(c)the coupling of agent-environment systems and (d) the necessity of real-time feedback signals from the environment. Under the FEP formulation, I will present a series of case studies with mainly two objectives in mind: 1) to conceptually analyse and reframe these 4E ideas in the context of active inference, arguing for the advantages of their formalisation in a more general probabilistic (Bayesian) framework and, 2) to present new mathematical models and agent-based implementations of some of the conceptual connections between Bayesian inference frameworks and 4E proposals, largely missing in the literature

On Neuromechanical Approaches for the Study of Biological Grasp and Manipulation

Biological and robotic grasp and manipulation are undeniably similar at the level of mechanical task performance. However, their underlying fundamental biological vs. engineering mechanisms are, by definition, dramatically different and can even be antithetical. Even our approach to each is diametrically opposite: inductive science for the study of biological systems vs. engineering synthesis for the design and construction of robotic systems. The past 20 years have seen several conceptual advances in both fields and the quest to unify them. Chief among them is the reluctant recognition that their underlying fundamental mechanisms may actually share limited common ground, while exhibiting many fundamental differences. This recognition is particularly liberating because it allows us to resolve and move beyond multiple paradoxes and contradictions that arose from the initial reasonable assumption of a large common ground. Here, we begin by introducing the perspective of neuromechanics, which emphasizes that real-world behavior emerges from the intimate interactions among the physical structure of the system, the mechanical requirements of a task, the feasible neural control actions to produce it, and the ability of the neuromuscular system to adapt through interactions with the environment. This allows us to articulate a succinct overview of a few salient conceptual paradoxes and contradictions regarding under-determined vs. over-determined mechanics, under- vs. over-actuated control, prescribed vs. emergent function, learning vs. implementation vs. adaptation, prescriptive vs. descriptive synergies, and optimal vs. habitual performance. We conclude by presenting open questions and suggesting directions for future research. We hope this frank assessment of the state-of-the-art will encourage and guide these communities to continue to interact and make progress in these important areas

NewtonianVAE: Proportional Control and Goal Identification from Pixels via Physical Latent Spaces

Learning low-dimensional latent state space dynamics models has been a powerful paradigm for enabling vision-based planning and learning for control. We introduce a latent dynamics learning framework that is uniquely designed to induce proportional controlability in the latent space, thus enabling the use of much simpler controllers than prior work. We show that our learned dynamics model enables proportional control from pixels, dramatically simplifies and accelerates behavioural cloning of vision-based controllers, and provides interpretable goal discovery when applied to imitation learning of switching controllers from demonstration