This is a quick advert for the excellent online course “Reinforcement Learning” by David Silver.

David Silver’s ‘teaching’ home page includes links to the slides (which are particularly helpful for Lecture 7, where there’s no video available - just sound).

These notes are mainly for my own consumption…

Musings : Eligibility Traces

Several things that bubbled to the surface during the Reinforcement Learning course:

  • Eligibility traces, which are a way of keeping track of how rewards for \(TD(\lambda)\) should be attributed to the states/actions that lead to them, seem very reminiscent of activation potentials

  • Aiming for minimum fit error is the same as optimising for least surprise, which is the same as making predictions that are as un-surprising as possible

  • Distributing the amount of ‘surprise’ (positive or negative) to exponentially decaying eligibility nodes with a neural network seems like a very natural reinterpretation of the \(TD(\lambda)\) framework

  • But current neural networks are densified, with multi-dimensional spaces embedding knowledge in a way that is entangled far more thoroughly than the sparse representations (apparently) found in the brain

  • Perhaps the ‘attribution problem’ that sparse & eligibility solves is equivalent to dense & backprop

  • But there appears to be a definite disconnect between the rationales behind each of the two methods that requires more justification

Musings : Exploration vs Exploitation

  • Interesting that \( (\mu + n\sigma) \) is an effective action-chooser, since that is what I was doing in the 1990s, but using as a placeholder heuristic until I found something that was ‘more correct’

  • But \([0,1]\) bounded i.i.d variables having a decent confidence bound (Hoeffding’s inequality) was a new thing for me

  • Also, liked the Thompson sampling (from 1930s) that implicitly created samples according to a distribution, merely by using samples from the underlying factors is very elegant

    • and makes me think about the heuristic in Genetic Algorithms for ‘just sampling’ as potentially solving a (very complex) probablity problem, without actually doing any computation

Musings : Games and State-of-the-Art

  • The tree optimisations seem ‘obvious’ in retrospect - but clearly each was a major ‘aha!’ when it was first proposed. Very interesting.

  • Almost all of the State-of-the-Art methods use binary features, linear approximations to \( v_*() \), search and self-play.

  • Perhaps deeper models will work instead of the linear ones - but it’s interesting that binary (~sparse?) features are basically powerful enough (when there’s some tree-search for trickier strategy planning)

Musings : Gimbal Learning

Lecture 8 of the Reinforcement Learning Course by David Silver is super-relevant to the Gimbal control problem that I’ve been considering.

It’s also interesting that the things I had already assumed would have been obvious are currently considered state-of-the-art (but isn’t that always the way? Hindsight, etc).

In summary :

  • Learn model from real world by observing state transitions, and then learning {state, action}-to-state mapping
    • Also learn {State, Action}-to-Reward mapping (almost a separate model)
  • Apply model-free methods to model-simulated world

  • Once ‘correct’ action has been selected, actually perform it

  • Now we have new real-world learning with which to fine-tune the world model

To apply this to gimbal, seems like one could present ‘target trajectories’ to controller in turn, letting it learn a common world-model, with different reward-models for each goal. And let it self-play…

Apropos of Nothing

DARPA Robotics Fast Track - are they doing anything?

Martin Andrews

{Finance, Software, AI} entrepreneur, living in Singapore with my family.

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