Probabilistic Reasoning Probabilistic Belief Learning Heuristic Search First, you need to formulate your situation as a Search Problem
What is a state? From one state, what other states can you get to (successor function)? For each of those transitions, what is the cost? Where is the start? What is the goal? Heuristic Search
Heuristic Search Easy to formulate for problems that are inherently discrete Solve a rubik's cube Given all the flights of the airlines, figure out the best way (time/distance/cost) to get from city A to city B What about problems that have continuous
spaces? Maneuvering a robot through a building Controlling a robot arm to do a task Heuristic Search Heuristic Search Heuristic Search Heuristic Search
No Heuristic DFS, BFS, Iterative Deepening, Uniform Cost Heuristic Have fringe sorted by f = g + h Admissibility
Consistency Planning Just a search problem! Use STRIPS to formulate the problem A state is a set of propositions which are true
Successor function given by Actions IN(Robot, R1), HOLDING(Apple) Preconditions (which are allowed) Add/Delete (what is the new state) How do we get a heuristic? Planning
Given some state s, how many actions will it take to get to a state satisfying g? Planning Graph Initialize to S0 all the proposition in s. Add the add lists of actions that apply to get S1 Repeat until convergence Find the first Si where the g is met
Planning Forward Planning Start initial node as initial state Find all successors by applying actions For each successor, build a planning graph to determine heuristic value
Construct planning graph from initial state Start initial node as goal Find successors by regressing through relevant actions Look up heuristic values in planning graph
Add to fringe, pop, repeat Constraint Satisfaction Formulation Variables, each with some domain Constraints between variables and their values
Problem: assign values to everything without violating any constraint Again, just a search problem (Backtracking) State: Partial assignment to variables Successor: Assign a value to next variable without violating anything Goal: All variables assigned
Constraint Satisfaction No sense of optimal path.. we just want to cut down on search time. How to choose variable to assign next? Most constrained variable Most constraining variable
How to choose the next value? Least constraining value Constraint Satisfaction To benefit from these heuristics, should update domains Forward Checking After assigning a value to a variable, remove all
conflicting values from other variables AC3 Given a set of variables, look at pairs X,Y If for a value of X, there is no value of Y that works, remove that value from X Adversarial Search Game tree from moves performed successively by MAX and MIN player
Values at bottom of the tree end of game, or use evaluation function. Propagate values up according to MIN/MAX Tells you which move to take Alpha-Beta pruning Order of evaluation does matter
Probabilistic Reasoning Assume there is some state space Now actions are probabilistic If I do action A, there are several different possible states I may end up in
There is a probability associated with going into each state (they must sum to 1) Some states have rewards (positive or negative) We would like to calculate utility for each state, and use that to determine what action to take. Probabilistic Reasoning Probabilistic Reasoning How do you calculate the Utilities? If no cycles, can back values up the tree
Otherwise, can use Value Iteration Start all utilities as 0, calculate new utilities, repeat until convergence Or, Policy Iteration Pick a random policy, solve utilities for it, calculate new policy until convergence Probabilistic Belief
Say N variables, each with 2 values, joint probability table has 2^n entries. Probabilistic Belief If variables are independent, can represent this table more compactly (Supervised) Learning
We are given a bunch of examples, where each example has values X1.. XN and Y We want to create some function H(X), that will take all the X's and output a single value The goal is that given some partial example X1... XN, we can use H(X) to guess Y This should work well for X's from the training set, but also for X's never seen before! (Supervised) Learning (Supervised) Learning Some types of functions we can use: Data Cache
Linear Regression Decision Tree Neural Net (Supervised) Learning
Decision Tree At each non-terminal node in tree, branch according to the value of one of the Xi's A leaf node should output a value for Y Building the Tree (Greedy) Look at all examples at current node Choose Xi to split on that will allow you to
classify the most number of examples correctly (Supervised) Learning Neural Net (Supervised) Learning Neural Net
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