Learning-Based Mean-Payoff Optimization in an Unknown MDP under Omega-Regular Constraints
| Autoři | |
|---|---|
| Rok publikování | 2018 |
| Druh | Článek ve sborníku |
| Konference | 29th International Conference on Concurrency Theory (CONCUR 2018) |
| Fakulta / Pracoviště MU | |
| Citace | |
| Doi | http://dx.doi.org/10.4230/LIPIcs.CONCUR.2018.8 |
| Klíčová slova | Learning; Mean-Payoff; Markov decision process; Omega-Regular Specification |
| Popis | We formalize the problem of maximizing the mean-payoff value with high probability while satisfying a parity objective in a Markov decision process (MDP) with unknown probabilistic transition function and unknown reward function. Assuming the support of the unknown transition function and a lower bound on the minimal transition probability are known in advance, we show that in MDPs consisting of a single end component, two combinations of guarantees on the parity and mean-payoff objectives can be achieved depending on how much memory one is willing to use. (i) For all epsilon and gamma we can construct an online-learning finite-memory strategy that almost-surely satisfies the parity objective and which achieves an epsilon-optimal mean payoff with probability at least 1 - gamma. (ii) Alternatively, for all epsilon and gamma there exists an online-learning infinite-memory strategy that satisfies the parity objective surely and which achieves an epsilon-optimal mean payoff with probability at least 1 - gamma. We extend the above results to MDPs consisting of more than one end component in a natural way. Finally, we show that the aforementioned guarantees are tight, i.e. there are MDPs for which stronger combinations of the guarantees cannot be ensured. |
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