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Towards on-line tuning of adaptive-agent’s multivariate meta-parameter

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Abstract

A decision-making (DM) agent models its environment and quantifies its DM preferences. An adaptive agent models them locally nearby the realisation of the behaviour of the closed DM loop. Due to this, a simple tool set often suffices for solving complex dynamic DM tasks. The inspected Bayesian agent relies on a unified learning and optimisation framework, which works well when tailored by making a range of case-specific options. Many of them can be made off-line. These options concern the sets of involved variables, the knowledge and preference elicitation, structure estimation, etc. Still, some meta-parameters need an on-line choice. This concerns, for instance, a weight balancing exploration with exploitation, a weight reflecting agent’s willingness to cooperate, a discounting factor, etc. Such options influence, often vitally, DM quality and their adaptive tuning is needed. Specific ways exist, for instance, a data-dependent choice of a forgetting factor serving to tracking of parameter changes. A general methodology is, however, missing. The paper opens a pathway to it. The solution uses a hierarchical feedback exploiting a generic, DM-related, observable, mismodelling indicator. The paper presents and justifies the theoretical concept, outlines and illustrates its use.

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Notes

  1. The prefix “meta” marks a task about a task, DM about DM, an option about an option, etc. Note that all abbreviations are summarised in Table 2 at the paper end.

  2. The agent’s prior knowledge \(k^{0}\) implicitly conditions all pds involved. The knowledge \(k^{t}\) is also called information state. \((o_{t},a_{t})_{t\in \varvec{\{}{t} \varvec{\}}}\) is often referred as (closed DM loop) trajectory or the observed behaviour.

  3. KLD, formerly called cross-entropy, Kullback and Leibler [67], now relative entropy, is the DM-rules-dependent expectation of the loss \(\ln (\mathsf {j}/\mathsf {j}_{\mathfrak {i}})\).

  4. The usual MDP deals with the reward \(-\mathsf {L}\) and maximises its expectation.

  5. This reflects its interpretation as a meta-action at the upper-level feedback, cf. Fig. 1 and Sect. 5.

  6. The same choice is faced when dealing with usual exploration techniques, Ouyang et al. [53].

  7. The term trust has narrower meaning than numerous studies focused on it, Li and Song [47].

  8. This form of Bayes’ rule is valid for the considered DM rules for which the parameter pointing to the “best” model, [4], is unknown, cf. natural conditions of control in Peterka [56].

  9. Extensive references on the whole approach can be found in the cited paper. The chapter, Dietrich and List [10], is a good starting point to pooling problems that are in the core of such a cooperation.

  10. In this context, Shannon’s sampling theorem, Shannon [66], provides no guide.

  11. The dependence of pds on the horizon h is made explicit here.

  12. For a pd \(\mathsf {s}\) on \(\varvec{\{}{x} \varvec{\}}\), its support \(\mathrm {supp}[\mathsf {s}]\equiv \{x\in \varvec{\{}{x} \varvec{\}}:\,\mathsf {s}(x)>0\}\).

  13. The proof tailors and refines results in Algoet and Cover [1, 4].

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  1. Institute of Information Theory and Automation, The Czech Academy of Sciences, 182 00, Prague 8, Czech Republic

    Miroslav Kárný

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The reported research has been supported by MŠMT ČR LTC18075 and EU-COST Action CA16228.

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Kárný, M. Towards on-line tuning of adaptive-agent’s multivariate meta-parameter. Int. J. Mach. Learn. & Cyber. 12, 2717–2731 (2021). https://doi.org/10.1007/s13042-021-01358-w

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