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Dennis Soemers provides an important point that from a theoretical standpoint, this can be seen as a non-issue. However, what you bring up is an important practical issue of potential-based reward shaping (PBRS). The issue is actually worse than you describe---it's more general than $s = s'$. In particular, the issue presents itself differently based on the ...

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I don't think the situation you're sketching should be a problem at all. If $P(s)$ is high (e.g. $P(s) = 1000$), this means (according to your shaping / "heuristic") that it's valuable to be in the state $s$, that you expect to be able to get high future returns from that state. If you then continuously take actions that keep you in the same state $s$, it ...

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Andrew Y. Ng (yes, that famous guy!) et al. proved, in the seminal paper Policy invariance under reward transformations: Theory and application to reward shaping (ICML, 1999), which was then part of his PhD thesis, that potential-based reward shaping (PBRS) is the way to shape the natural/correct sparse reward function (RF) without changing the optimal ...

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The same $\gamma = 0.9$ that you use in the definition $F \doteq \gamma \Phi(s') - \Phi(s)$ should also be used as the discount factor in computing returns for multi-step trajectories. So, rather than simply adding up all the rewards for your different time-steps for the different trajectories, you should discount them by $\gamma$ for every time step that ...

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Is the method itself defective or anything wrong with my code? There does indeed appear to be an issue with the code, the publications are fine (I know most of those authors and would very much trust their writing too :) ). The first issue I see, and likely the most important, is that the update() calls of DynamicPBA frequently update the contents of self....

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