AGENTS AND ENVIRONMENTS

Environment types Fully observable (vs. partially observable): An

agent's sensors give it access to the complete state of the environment at each point in time.

Deterministic (vs. stochastic): The next state of the environment is completely determined by the current state and the action executed by the agent.

Episodic (vs. sequential): The agent's experience is divided into atomic "episodes" (each episode consists of the agent perceiving and then performing a single action), and the choice of action in each episode depends only on the episode itself.

Environment types Static (vs. dynamic): The environment is

unchanged while an agent is deliberating. Discrete (vs. continuous): A limited number

of distinct, clearly defined percepts and actions.

Single agent (vs. multiagent): An agent operating by itself in an environment.

Adversarial (vs. benign): There is an opponent in the environment who actively trying to thwart you.

Example Some of these descriptions can be ambiguous,

depending on your assumptions and interpretation of the domainContinuo

usStochastic

Partially Observable

Adversarial

Chess, CheckersRobot SoccerPokerHide and SeekCards SolitaireMinesweeper

Environment typesChess with Chess without

Taxi driving a clock a clock

Fully observable Yes Yes No Deterministic Yes Yes No Episodic No No No Static Semi Yes No Discrete Yes Yes NoSingle agent No No No?

The real world is partially observable, stochastic, sequential, dynamic, continuous, multi-agent

GAMES(I.E. ADVERSARIAL

SEARCH)

Games vs. search problems Search: only had to worry about your

actions Games: opponent’s moves are often

interspersed with yours, need to consider opponent’s action

Games typically have time limits Often, an ok decision now is better than a

perfect decision later

Games Card games Strategy games FPS games Training games …

Single Player, Deterministic Games

Two-Player, Deterministic, Zero-Sum Games

Zero-sum: one player’s gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of other player(s) E.g., chess, checkers, rock-paper-scissors,

…

Two-Player, Deterministic, Zero-Sum Games : the initial state : defines which player has the move in a state : defines the set of legal moves : the transition model that defines the result of

the move : returns true if the game is over. In that case

is called a terminal state. : a utility function (objective function) that

defines the numeric value of the terminal state for player

Minimax

Game tree (2-player, deterministic, turns)

Minimax

Minimax “Perfect play” for deterministic games Idea: choose move to position with highest

minimax value = best achievable payoff against best play

Is minimax optimal? Depends

If opponent is not rational could be a better play

Yes With assumption both players always make

best move

Properties of minimax Complete?

Yes (if tree is finite)

Space complexity? O(bd) (depth-first exploration)

Optimal? Yes (against an optimal opponent)

Time complexity? O(bd)

For chess, b ≈ 35, d ≈100 for "reasonable" games

≈ 10154

exact solution completely infeasible

How to handle suboptimal opponents?

Can build model of opponent behavior Use that to guide search rather than MIN

Reinforcement learning (later in the semester) provides another approach

α-β pruning Do we need to explore every node in the

search tree?

Insight: some moves are clearly bad choices

α-β pruning example

α-β pruning example

What is the value of this node?

And this one?

First option is worth 3, so root is at least that good

Now consider the second option

What is this node worth?

At most 2

But, what if we had these values?

1 99

It doesn’t matter, they won’t make any difference so don’t look at them.

α-β pruning example

α-β pruning example

α-β pruning example

Why didn’t we check this node first?

Properties of α-β Pruning does not affect final result

i.e. returns the same best move (caveat: only if can search entire tree!)

Good move ordering improves effectiveness of pruning

With "perfect ordering," time complexity = O(bm/2) Can come close in practice with various heuristics

Bounding search Similar to depth-limited search:

Don’t have to search to a terminal state, search to some depth instead

Find some way of evaluating non-terminal states

Evaluation function Way of estimating how good a position is

Humans consider (relatively) few moves and don’t search very deep

But they can play many games well evaluation function is key

A LOT of possibilities for the evaluation function

A simple function for chess White = 9 * # queens + 5 *# rooks + 3 *

# bishops + 3 * # knights + # pawns Black= 9 * # queens + 5 *# rooks + 3 *

# bishops + 3 * # knights + # pawns

Utility= White - Black

Other ways of evaluating a game position?

Features: Spaces you control How compressed your pieces are Threat-To-You – Threat-To-Opponent How much does it restrict opponent options

Interesting ordering

Game Branching factor Computer qualityGo 360 << human

Chess 35 ≈ humanOthello 10 >> human

Implications

Game Branching factor Computer qualityGo 360 << human

Chess 35 ≈ humanOthello 10 >> human

• Larger branching factor (relatively) harder for computers

• People rely more on evaluation function than on search

Deterministic games in practice

Othello: human champions refuse to compete against computers, who are too good.

Chess: Deep Blue defeated human world champion Garry Kasparov in a six-game match in 1997.

Checkers: Chinook ended 40-year-reign of human world champion Marion Tinsley in 1994. In 2007 developers announced that the program has been improved to the point where it cannot lose a game.

Go: human champions refuse to compete against computers, who are too bad.

More on checkers

Checkers has a branching factor of 10 Why isn’t the result like Othello?

Complexity of imagining moves: a move can change a lot of board positions A limitation that does not affect computers

Game Branching factor Computer qualityGo 360 << human

Chess 35 ≈ humanOthello 10 >> human

Summary Games are a core (fun) part of AI

Illustrate several important points about AI Provide good visuals and demos

Turn-based games (that can fit in memory) are well addressed

Make many assumptions (optimal opponent, turn-based, no alliances, etc.)

Questions?