13 research outputs found
Realising Synthetic Active Inference Agents, Part II: Variational Message Updates
The Free Energy Principle (FEP) describes (biological) agents as minimising a
variational Free Energy (FE) with respect to a generative model of their
environment. Active Inference (AIF) is a corollary of the FEP that describes
how agents explore and exploit their environment by minimising an expected FE
objective. In two related papers, we describe a scalable, epistemic approach to
synthetic AIF agents, by message passing on free-form Forney-style Factor
Graphs (FFGs). A companion paper (part I) introduces a Constrained FFG (CFFG)
notation that visually represents (generalised) FE objectives for AIF. The
current paper (part II) derives message passing algorithms that minimise
(generalised) FE objectives on a CFFG by variational calculus. A comparison
between simulated Bethe and generalised FE agents illustrates how synthetic AIF
induces epistemic behaviour on a T-maze navigation task. With a full message
passing account of synthetic AIF agents, it becomes possible to derive and
reuse message updates across models and move closer to industrial applications
of synthetic AIF
Variational message passing for online polynomial NARMAX identification
We propose a variational Bayesian inference procedure for online nonlinear
system identification. For each output observation, a set of parameter
posterior distributions is updated, which is then used to form a posterior
predictive distribution for future outputs. We focus on the class of polynomial
NARMAX models, which we cast into probabilistic form and represent in terms of
a Forney-style factor graph. Inference in this graph is efficiently performed
by a variational message passing algorithm. We show empirically that our
variational Bayesian estimator outperforms an online recursive least-squares
estimator, most notably in small sample size settings and low noise regimes,
and performs on par with an iterative least-squares estimator trained offline.Comment: 6 pages, 4 figures. Accepted to the American Control Conference 202
AIDA: An Active Inference-based Design Agent for Audio Processing Algorithms
In this paper we present AIDA, which is an active inference-based agent that iteratively designs a personalized audio processing algorithm through situated interactions with a human client. The target application of AIDA is to propose on-the-spot the most interesting alternative values for the tuning parameters of a hearing aid (HA) algorithm, whenever a HA client is not satisfied with their HA performance. AIDA interprets searching for the "most interesting alternative" as an issue of optimal (acoustic) context-aware Bayesian trial design. In computational terms, AIDA is realized as an active inference-based agent with an Expected Free Energy criterion for trial design. This type of architecture is inspired by neuro-economic models on efficient (Bayesian) trial design in brains and implies that AIDA comprises generative probabilistic models for acoustic signals and user responses. We propose a novel generative model for acoustic signals as a sum of time-varying auto-regressive filters and a user response model based on a Gaussian Process Classifier. The full AIDA agent has been implemented in a factor graph for the generative model and all tasks (parameter learning, acoustic context classification, trial design, etc.) are realized by variational message passing on the factor graph. All verification and validation experiments and demonstrations are freely accessible at our GitHub repository
Ergodicity-breaking reveals time optimal decision making in humans
Ergodicity describes an equivalence between the expectation value and the
time average of observables. Applied to human behaviour, ergodic theories of
decision-making reveal how individuals should tolerate risk in different
environments. To optimise wealth over time, agents should adapt their utility
function according to the dynamical setting they face. Linear utility is
optimal for additive dynamics, whereas logarithmic utility is optimal for
multiplicative dynamics. Whether humans approximate time optimal behavior
across different dynamics is unknown. Here we compare the effects of additive
versus multiplicative gamble dynamics on risky choice. We show that utility
functions are modulated by gamble dynamics in ways not explained by prevailing
decision theory. Instead, as predicted by time optimality, risk aversion
increases under multiplicative dynamics, distributing close to the values that
maximise the time average growth of wealth. We suggest that our findings
motivate a need for explicitly grounding theories of decision-making on ergodic
considerations.Comment: 43 pages including supplementary methods & material
A Worked Example of Fokker-Planck based Active Inference
The Free Energy Principle (FEP) and its corollary active inference describe a complex theoretical framework with a substantial statistical mechanics foundation that is often expressed in terms of the Fokker-Planck equation. Easy-to-follow examples of this formalism are scarce, leaving a high barrier of entry to the field. In this paper we provide a worked example of an active inference agent as a hierarchical Gaussian generative model. We proceed to write its equations of motion explicitly as a Fokker-Planck equation, providing a clear mapping between theoretical accounts of FEP and practical implementation. Code is available at github.com/biaslab/ai_workshop_2020.</p
BATMAN: BAyesian Target Modelling for Active iNference
Active Inference is an emerging framework for designing intelligent agents. In an Active Inference setting, any task is formulated as a variational free energy minimisation problem on a generative probabilistic model. Goal-directed behaviour relies on a clear specification of desired future observations. Learning desired observations would open up the Active Inference approach to problems where these are difficult to specify a priori. This paper introduces the BAyesian Target Modelling for Active iNference (BATMAN) approach, which augments an Active Inference agent with an additional, separate model that learns desired future observations from a separate data source. The main contribution of this paper is the design of a coupled generative model structure that facilitates learning desired future observations for Active Inference agents and supports integration of Active Inference and classical methods in a joint framework. We provide proof-of-concept validation for BATMAN through simulations
Variational message passing for online polynomial NARMAX identification
We propose a variational Bayesian inference procedure for online nonlinear system identification. For each output observation, a set of parameter posterior distributions is updated, which is then used to form a posterior predictive distribution for future outputs. We focus on the class of polynomial NARMAX models, which we cast into probabilistic form and represent in terms of a Forney-style factor graph. Inference in this graph is efficiently performed by a variational message passing algorithm. We show empirically that our variational Bayesian estimator outperforms an online recursive least-squares estimator, most notably in small sample size settings and low noise regimes, and performs on par with an iterative least-squares estimator trained offline
Realising Synthetic Active Inference Agents, Part I: Epistemic Objectives and Graphical Specification Language
The Free Energy Principle (FEP) is a theoretical framework for describing how
(intelligent) systems self-organise into coherent, stable structures by
minimising a free energy functional. Active Inference (AIF) is a corollary of
the FEP that specifically details how systems that are able to plan for the
future (agents) function by minimising particular free energy functionals that
incorporate information seeking components. This paper is the first in a series
of two where we derive a synthetic version of AIF on free form factor graphs.
The present paper focuses on deriving a local version of the free energy
functionals used for AIF. This enables us to construct a version of AIF which
applies to arbitrary graphical models and interfaces with prior work on message
passing algorithms. The resulting messages are derived in our companion paper.
We also identify a gap in the graphical notation used for factor graphs. While
factor graphs are great at expressing a generative model, they have so far been
unable to specify the full optimisation problem including constraints. To solve
this problem we develop Constrained Forney-style Factor Graph (CFFG) notation
which permits a fully graphical description of variational inference
objectives. We then proceed to show how CFFG's can be used to reconstruct prior
algorithms for AIF as well as derive new ones. The latter is demonstrated by
deriving an algorithm that permits direct policy inference for AIF agents,
circumventing a long standing scaling issue that has so far hindered the
application of AIF in industrial settings. We demonstrate our algorithm on the
classic T-maze task and show that it reproduces the information seeking
behaviour that is a hallmark feature of AIF.Comment: 49 pages, 31 figure
On Epistemics in Expected Free Energy for Linear Gaussian State Space Models
Active Inference (AIF) is a framework that can be used both to describe information processing in naturally intelligent systems, such as the human brain, and to design synthetic intelligent systems (agents). In this paper we show that Expected Free Energy (EFE) minimisation, a core feature of the framework, does not lead to purposeful explorative behaviour in linear Gaussian dynamical systems. We provide a simple proof that, due to the specific construction used for the EFE, the terms responsible for the exploratory (epistemic) drive become constant in the case of linear Gaussian systems. This renders AIF equivalent to KL control. From a theoretical point of view this is an interesting result since it is generally assumed that EFE minimisation will always introduce an exploratory drive in AIF agents. While the full EFE objective does not lead to exploration in linear Gaussian dynamical systems, the principles of its construction can still be used to design objectives that include an epistemic drive. We provide an in-depth analysis of the mechanics behind the epistemic drive of AIF agents and show how to design objectives for linear Gaussian dynamical systems that do include an epistemic drive. Concretely, we show that focusing solely on epistemics and dispensing with goal-directed terms leads to a form of maximum entropy exploration that is heavily dependent on the type of control signals driving the system. Additive controls do not permit such exploration. From a practical point of view this is an important result since linear Gaussian dynamical systems with additive controls are an extensively used model class, encompassing for instance Linear Quadratic Gaussian controllers. On the other hand, linear Gaussian dynamical systems driven by multiplicative controls such as switching transition matrices do permit an exploratory drive
Gaussian Process-based Amortization of Variational Message Passing Update Rules
Variational Message Passing facilitates automated variational inference in factorized probabilistic models where connected factors are conjugate pairs. Conjugate-computation Variational Inference (CVI) extends the applicability of VMP to models comprising both conjugate and non-conjugate factors. CVI makes use of a gradient that is estimated by Monte Carlo (MC) sampling, which potentially leads to substantial computational load. As a result, for models that feature a large number of non-conjugate pairs, CVI-based inference may not scale well to larger model sizes. In this paper, we propose a Gaussian Process-enhanced CVI approach, called GP-CVI, to amortize the computational costs caused by the MC sampling procedures in CVI. Specifically, we train a Gaussian process regression (GPR) model based on a set of incoming outgoing message pairs that were generated by CVI. In operation, we use the “cheaper” GPR model to produce outgoing messages and resort to the more accurate but expensive CVI message only if the variance of the outgoing message exceeds a threshold. By experimental validation, we show that GP-CVI gradually uses more fast memory-based update rule computations, and less sampling-based update rule computations. As a result, GP-CVI speeds up CVI with a controllable effect on the accuracy of the inference procedure