Mcts Backpropagate

Statistics Update

For each node in the path from leaf to root:

node.N += 1
node.Q += reward
node.avg_reward = node.Q / node.N

Backpropagation Strategy

For the current context: $ARGUMENTS

Standard Update

• Each node gets the same reward
• Simple and effective for most problems

Discounted Update (optional)

• Apply discount factor γ as you go up
• Nodes closer to outcome get more credit
• node.Q += reward * (γ ^ depth_from_leaf)

Observation Recording

After backpropagation:

1. Record any new insights as observations
2. Update beliefs if the result was surprising
3. Note if any branch is now clearly best/worst

Convergence Check

After updating, check:

1. Best path stability: Has the best path changed?
2. Value convergence: Are top nodes' values stabilizing?
3. Sufficient exploration: Have all branches been tried?

Output

After backpropagation, report:

1. Nodes updated with new statistics
2. Current best path and its average reward
3. Exploration coverage (% of nodes visited)
4. Whether to continue or extract solution

If continuing, return to SELECTION phase. If converged or budget exhausted, extract the solution.