class: center, middle, inverse, title-slide .title[ # RL in action ] .author[ ### Lars Relund Nielsen ] --- layout: true <div class="my-footer"> <span> <a href="https://bss-osca.github.io/rl/sec-rl-in-action.html" target="_blank">Notes</a> | <a href="https://bss-osca.github.io/rl/slides/03_rl-in-action-slides.html" target="_blank">Slides</a> | <a href="https://github.com/bss-osca/rl/blob/master/slides/03_rl-in-action-slides.Rmd" target="_blank">Source</a> </span> </div> --- ## Learning outcomes * Identify the blocks of a RL model (environment, agent, data, states, actions, rewards and policies) on a specific problem. * Define the value function for the problem. * Code your first RL algorithm. * Evaluate on the solution. --- ## Let's play Tic-Tac-Toe We start with an empty board and have at most 9 moves (a player may win before). The player who succeeds in placing three of their marks in a horizontal, vertical, or diagonal row wins the game. Reward for a player is 1 for 'win', 0.5 for 'draw', and 0 for 'loss'. These values can be seen as the probability of winning. <table style="width: 100%; border: 0px !important;"> <tr> <td><table border: solid black class="table table-bordered" style="width: auto !important; margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="text-align:center;"> . </td> <td style="text-align:center;"> . </td> <td style="text-align:center;"> X </td> </tr> <tr> <td style="text-align:center;"> . </td> <td style="text-align:center;"> X </td> <td style="text-align:center;"> . </td> </tr> <tr> <td style="text-align:center;"> X </td> <td style="text-align:center;"> O </td> <td style="text-align:center;"> O </td> </tr> </tbody> </table> </td> <td><table border: solid black class="table table-bordered" style="width: auto !important; margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="text-align:center;"> X </td> <td style="text-align:center;"> . </td> <td style="text-align:center;"> X </td> </tr> <tr> <td style="text-align:center;"> . </td> <td style="text-align:center;"> X </td> <td style="text-align:center;"> . </td> </tr> <tr> <td style="text-align:center;"> O </td> <td style="text-align:center;"> O </td> <td style="text-align:center;"> O </td> </tr> </tbody> </table> </td> <td><table border: solid black class="table table-bordered" style="width: auto !important; margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="text-align:center;"> X </td> <td style="text-align:center;"> X </td> <td style="text-align:center;"> O </td> </tr> <tr> <td style="text-align:center;"> O </td> <td style="text-align:center;"> O </td> <td style="text-align:center;"> X </td> </tr> <tr> <td style="text-align:center;"> X </td> <td style="text-align:center;"> X </td> <td style="text-align:center;"> O </td> </tr> </tbody> </table> </td> </tr> </table> --- ## Gameplay Let `\(S_t\)` denote the board state before the opponent makes a move. <img src="img/rl-in-action-hgf-1.png" width="100%" height="80%" style="display: block; margin: auto;" /> --- ## Learning to play - Define `\(V(S)\)` to be 1 if we win, 0 if we loose and 0.5 otherwise (reward/pr of winning). - Most of the time we *exploit* our knowledge with `\(pr = 1-\epsilon\)`, i.e. choose the action which gives us the highest estimated reward and update the value of a state using `$$\begin{align}V(S_t) &= V(S_t) + \alpha(V(S_{t+1})-V(S_t)) \\&= (1-\alpha)V(S_t) + \alpha V(S_{t+1})\end{align}$$` where `\(\alpha\)` is the *step-size* parameter. - Some times we *explore* with `\(pr = \epsilon\)` and choose another action/move than what seems optimal. --- ## Let us have a look at the code - Open the [Tic-tac-toe][colab-03-rl-in-action] notebook. 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