Trade off between Exploration and Exploitation in Satisficing Planning Fan Xie

Outline What is Satisficing Planning Heuristic Search in Planning Why we need exploration? Analysis of Arvand Arvand-LTS: Arvand with Local MCTS Experiments

Outline What is Satisficing Planning Heuristic Search in Planning Why we need exploration? Analysis of Arvand Arvand-LTS: Arvand with Local MCTS Experiments

AI Planning

Satisficing Planning Deterministic environment Only require sub-optimal solutions Domain Independent Planning Implicit Representation of the search space (why not explicit representation?) Impossible in most cases, because of huge state space Example: An initial state: s0 A set of actions: A A set of requirements of a goal state: G

Outline What is Satisficing Planning Heuristic Search in Planning Why we need exploration? Analysis of Arvand Arvand-LTS: Arvand with Local MCTS Experiments

Some Background What is a Heuristic? Here, tell you how close this node to objects Greedy Best-First Search: When expanding node n, take each successor n' and place it on one list ordered by h(n’) Hill Climbing Search: check neighbor nodes of current node, select the node has lower h-value than current node. (if many, the lowest) Terminates when no neighbor node has lower h-value

Heuristic Search As Planning FF Planner Hill climbing FF heuristic: not admissble Enforced Hill climbing: more exploration in hill climbing to escape from local mimima LAMA Planner Greedy Best-First Search (WA*) Mixed heuristic: FF+Landmark

Outline What is Satisficing Planning Heuristic Search in Planning Why we need exploration? Analysis of Arvand Arvand-LTS: Arvand with Local MCTS Experiments

Why we need exploration? Best First Search and Hill Climbing, mostly do greedy exploitation. Problem: Local Minima and Plateaus

Local Minima and Plateaus Local minima: local best h-value Plateaus: an area all nodes have the same h-value

More Exploration Current algorithms or planners directly address the tradeoff between exploration and exploitation: RRT(not for satisficing planning) Identidem (stochastic hill climbing) Diverse best-first search (not published yet) Arvand (Monte-Carlo random walk)

Rapidly-Exploring Random Tree(RRT) RRT gradually builds a tree in the search space until a path to the goal state is found. At each step the tree is either expanded towards the goal, which corresponds to exploitation, or towards a randomly selected point in the search space for exploration

RRT example

RRT RRT requires complete model of the environment to generate random points for exploration. However, current planning domains mostly provide implicit representation of the search space. Random points might be invalid. (one possible way to do is assume it is valid) Distribution of random points is not uniformed.

Identidem Coles and Smith’s Identidem introduces exploration by stochastic local search (SLS). Algorithm: Local search action sequences chosen probabilistically from the set of all possible actions in each state evaluates the FF heuristic after each action and immediately jumps to the first state that improves on the start state

Diverse best-first search (DBFS) diversify search directions by probabilistically selecting a node that does not have the best heuristic estimate （ not published yet ） DBFSGBFSKBFS # Solved(1612) 1451 (161) 1209 (403) 1288 (324)

Arvand Exploration using random walks helps to overcome the problem of local minima and plateaus. Jumping greedily exploits the knowledge gained by the random walks. Diff with Identidem: only the end-states of random walks are evaluated

Outline What is Satisficing Planning Heuristic Search in Planning Why we need exploration? Analysis of Arvand Arvand-LTS: Arvand with Local MCTS Experiments

Analysis of Arvand Fast Exploration: Exploration using random walks Only end-states evaluated makes faster exploration (computing heuristic value takes 90% of time) Greedy Exploitation: Jump to the best obtained node

Advantages of Arvand escape from local minima and plateaus and quickly

Coverage of Arvand(current ipc problems not hard enough) ArvandLAMAFFFast Downward # Solved(1782) 1641 (92%) 1581 (89%) 1389 (78%) 1374 (77%)

Still some problem Problem: Waste a lot of knowledge Sometimes a lot of duplications

Outline What is Satisficing Planning Heuristic Search in Planning Why we need exploration? Analysis of Arvand Arvand-LTS: Arvand with Local MCTS Experiments

Arvand-LTS: Arvand with Local MCTS Motivation: Use more knowledge we get from random walks? Selectively growing a search tree while running random walks

Monte-Carlo Random Walk-based Local Tree Search (MRW-LTS)

Framework of MCTS

MRW-LTS Every local search build a local search tree Random walks are required starting from leaf nodes of the search tree. Nodes in tree store the minimum h-value obtained by random walks starting from their subtrees (not node h- value) It selects a leaf node by following an ε-greedy strategy in each node.

Some Change

Outline What is Satisficing Planning Heuristic Search in Planning Why we need exploration? Analysis of Arvand Arvand-LTS: Arvand with Local MCTS Experiments

1, IPC , big search spaces

Coverage on IPC-6 DomainsLAMAArvand Arvand-LTS Cyber 100% Elevator 87% 100% Openstacks 100% Parcprinter 77% 100% Pegsols 100% Scanalyzer 100% 90% Transport 100% Woodworking 100% Total 96% 99%

Coverage

Summary 1, exploration is important in satisficing planning 2, A good balancing between exploration and exploitation might make a big difference!