Visualized learning9/3/2023 ![]() ![]() Download a PDF of the paper titled Reflections and Considerations on Running Creative Visualization Learning Activities, by Jonathan C. """ def choose ( self, state ): return random. Heustics can be used here to improve simulations. time () return root_node """ Create a root node representing an initial state """ def create_root_node ( self ): abstract """ Choose a random action. back_propagate ( reward, child ) current_time = time. is_terminal ( selected_node ): child = selected_node. time () while current_time < start_time + timeout : # Find a state node to expand selected_node = root_node. bandit = bandit """ Execute the MCTS algorithm from the initial state given, with timeout in seconds """ def mcts ( self, timeout = 1, root_node = None ): if root_node is None : root_node = self. visits class MCTS : def _init_ ( self, mdp, qfunction, bandit ): self. state ) ) return max_q_value """ Get the number of visits to this state """ def get_visits ( self ): return Node. action = action """ Select a node that is not fully expanded """ def select ( self ): abstract """ Expand a node if it is not a terminal node """ def expand ( self ): abstract """ Backpropogate the reward back to the parent node """ def back_propagate ( self, reward, child ): abstract """ Return the value of this node """ def get_value ( self ): ( _, max_q_value ) = self. reward = reward # The action that generated this node self. bandit = bandit # The immediate reward received for reaching this state, used for backpropagation self. qfunction = qfunction # A multi-armed bandit for this node self. next_node_id += 1 # The Q function used to store state-action values self. Import math import time import random from collections import defaultdict class Node : # Record a unique node id to distinguish duplicated states next_node_id = 0 # Records the number of times states have been visited visits = defaultdict ( lambda : 0 ) def _init_ ( self, mdp, parent, state, qfunction, bandit, reward = 0.0, action = None ): self. Note that this is not a model-free approach: we still need a model in the form of a simulator, but we do not need to have explicit tranisition and reward functions. ![]() Over many simulations, the Select (and Expand/Execute steps) will sample \(P_a(s' \mid s)\) sufficiently close that \(Q(s,a)\) will converge to the average expected reward. using a code-based simulator, then this does not matter. Provided that we can simulate the outcomes e.g. This is why the tree is called an ExpectiMax tree: we maximise the expected return.īut: what if we do not know \(P_a(s' \mid s)\)? \(\quad\quad\) \(a \leftarrow \) parent action of \(s\)īecause action outcomes are selected according to \(P_a(s' \mid s)\), this will converge to the average expected reward. \(\quad\quad\) \(s \leftarrow \) parent of \(s\) The quality of each action \(a\) is approximated by averaging the expected reward of trajectories over \(S\) obtained by repeated simulations, giving as an approximation for \(Q(s,a)\). As such, planning and execution are interleaved such that:įor each state \(s\) visited, the set of all available actions \(A(s)\) partially evaluated Once an action (or perhaps a sequence of actions) is executed, we start planning again from the new state. ![]() In online planning, planning is undertaken immediately before executing an action. ![]()
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