Dynamic Fuzzy Machine Learning

The agent would like to obtain the different reward values $(\overleftarrow{r_t^i},\overrightarrow{r_t^i})(1\le i\le m)$ and the final reward value set $(\overleftarrow{r_t},\overrightarrow{r_t})=\{(\overleftarrow{r_t^1},\overrightarrow{r_t^1}),(\overleftarrow{r_t^1},\overrightarrow{r_t^1}),\mathrm{...}(\overleftarrow{r_t^m},\overrightarrow{r_t^m})\}$ by taking different actions $a_t^i(1\le i\le m).$ Thus, the agent will select the peak value in the set, defined as $(\overleftarrow{r_t^{\max }},r_t^{\max })(1\le \max \le m).$ Based on the peak reward value, the agent will obtain the corresponding action $a_t^{\max }(1\le \max \le m).$ Therefore, the current state of the agent will be converted from $({\overleftarrow{S}}_t,\overrightarrow{S_t})\text{to}({\overleftarrow{S}}_{t+1},\overrightarrow{S_{t+1}}).$ Overall, the formulation of the learning process of the agent can be represented as $\begin{array}{l}(\stackrel{}{R_{}}\end{array}$