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I need the q-value for my RL training, there are some approaches:

  • Brute-force the action sequence (this won't work for long sequence)
  • Use a classic algorithm to optimise and estimate (this ain't much AI)
  • Create Monte Carlo samples and train an approximator network for calculating q-value

I find the Monte Carlo method above rather widely applicable to different problems, and the more computing power, the more precise it is. Any other methods for calculating q-value?

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    $\begingroup$ How much RL do you know? When you say classic algorithms do you mean Dynamic Programming algorithms? $\endgroup$ – David Ireland Feb 1 at 13:30
  • $\begingroup$ anything, not just dynamic programming. i can use some kind of greedy and random optimisation for the action sequence after the action in q(s,a); that's what i meant about 'classic algo' $\endgroup$ – datdinhquoc Feb 1 at 13:51
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    $\begingroup$ Do you know any existing RL methods, such as Q-learning, SARSA? If I knew your existing knowledge of RL it would be easier to answer the question. $\endgroup$ – David Ireland Feb 1 at 14:59
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    $\begingroup$ @datdinhquoc To me, this question is not fully clear (e.g. I don't understand what you mean by "Brute-force the action sequence"), so I agree with David that you should describe what you know about RL, and why you're trying to estimate a Q-table without apparently wanting to use RL algorithms, such as Q-learning. When we use "approximation" in RL we typically mean function approximation, but it doesn't seem that you meant that. You just want to "estimate" the state-action value function, apparently. So, what is your question? Are you asking which algorithms are there to estimate Q(s, a)? $\endgroup$ – nbro Feb 1 at 17:36
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    $\begingroup$ @datdinhquoc Why don't you simply use Q-learning? $\endgroup$ – nbro Feb 2 at 18:56
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There's are some solutions to calculating q-values; find the exact values:

  • Brute-force the action sequence to find max (not pratical)
  • Do recursion on Bellman equation to get max (the same like action sequence brute-force, not pratical)

Estimate the q-values:

  • Based on different problems to solve, apply some classic algorithms or human logics to estimate; during estimation, some heuristic tactics may be used
  • Do a lot of randomisation to find max, including Monte Carlo tree search

Gradually optimise the q-values:

(1) Do optimisation based on Bellman equation (Q-learning): $$ q_t(s_t,a_t) = q_t(s_t,a_t) + \alpha(r + \gamma\times\max(q_{t+1}(s_{t+1},a_{t+1})) - q_t(s_t,a_t))$$

Bellman equation is true when the temporal difference (the part multiplied with $\alpha$) reaches zero, which means the max of time t+1 reaches exact value.

(2) Do optimisation based on Bellman equation (Q-network), fit the neural network to expected value: $$r + \gamma\times\max(q_{t+1}(s_{t+1},a_{t+1}))$$

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