General Value Functions

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General value functions (GVFs) are a generalization of value functions to predict signals other than the reward. They were introduced in (Sutton et al. 2011) and further explored in (Modayil, White, and Sutton 2014; White 2015), where the authors demonstrated their capabilities on a robot system (the critterbot). The goal of this demonstration was to show what can be learned using GVFs, and how the prediction making capabilities scale computationally.

A GVF is defined as the expected discounted return of a cumulant:

\[ v_{c, \gamma, \pi}(s) = \expected\left[\sum_{k=t}^\infty \left(\prod_{i=t+1}^k \gamma(S_i)\right) c_{k+1} \middle| S_t = s, A_{t:\infty} \sim \pi\right]. \]

• Cumulant (\(c\))

  The cumlant is a function of any real-valued signal the agent has access to. Some possible values

  • Observations
  • Reward
  • Other predictions
  • Agent-state.

  This is like the reward function, and details what signal the GVF is predicting.

• Continuation function (\(\gamma\))

  The continuation function (also known as the discount or termination function) and defines the temporal horizon of the prediction. This function should have values \(\in [0,1]\), and for at least one state the value must be \(<1\).

• Policy (\(\pi\))

  The policy determines the prediction’s target policy. Off-policy prediction is an important factor in GVFs, and when thinking about the predictions in terms of knowledge off-policy predictions can be seen as a form of counter-factual reasoning as it enables the agent to “think” or make predictions about different ways of acting.

Uses

General value functions are relatively new. Unfortunately, there have not been a lot of uses of GVFs explored in literature.

General Value Function Networks (GVFNs)

This work was spearheaded by me in (Schlegel et al. 2021). The main idea is to constrict the hidden state of an RNN to GVFs.

General Value Functions for Auxiliary Tasks

Predicting Surprise

Estimating variance

References