Reinforcement Learning ICS 273A Instructor: Max Welling Source: T. Mitchell, Machine Learning, Chapter 13.Overview • Supervised Learning: Immediate feedback (labels provided for every input. • Unsupervised Learning: No feedback (no labels provided). • Reinforcement Learning: Delayed scalar feedback (a number called reward). • RL deals with agents that must sense & act upon their environment. This is combines classical AI and machine learning techniques. It the most comprehensive problem setting. • Examples: • A robot cleaning my room and recharging its battery • Robot-soccer • How to invest in shares • Modeling the economy through rational agents • Learning how to fly a helicopter • Scheduling planes to their destinations • and so onThe Big Picture Your action influences the state of the world which determines its rewardComplications • The outcome of your actions may be uncertain • You may not be able to perfectly sense the state of the world • The reward may be stochastic. • Reward is delayed (i.e. finding food in a maze) • You may have no clue (model) about how the world responds to your actions. • You may have no clue (model) of how rewards are being paid off. • The world may change while you try to learn it • How much time do you need to explore uncharted territory before you exploit what you have learned?The Task • To learn an optimal policy that maps states of the world to actions of the agent. I.e., if this patch of room is dirty, I clean it. If my battery is empty, I recharge it. • What is it that the agent tries to optimize? Answer: the total future discounted reward: Note: immediate reward is worth more than future reward. What would happen to mouse in a maze with gamma = 0 ?Value Function • Let’s say we have access to optimal value function that computes the total future discounted reward • What would be the optimal policy ? • Answer: we choose the action that maximizes: • We assume that we know what the reward will be if we perform action “a” in state “s”: • We also assume we know what the next state of the world will be if we perform action “a” in state “s”:Example I • Consider some complicated graph, and we would like to find the shortest path from a node Si to a goal node G. • Traversing an edge will cost you “length edge” dollars. • The value function encodes the total remaining distance to the goal node from any node s, i.e. V(s) = “1 / distance” to goal from s. • If you know V(s), the problem is trivial. You simply choose the node that has highest V(s). Si GExample II Find your way to the goal.Q-Function • One approach to RL is then to try to estimate V*(s). • However, this approach requires you to know r(s,a) and delta(s,a). • This is unrealistic in many real problems. What is the reward if a robot is exploring mars and decides to take a right turn? • Fortunately we can circumvent this problem by exploring and experiencing how the world reacts to our actions. We need to learn r & delta. • We want a function that directly learns good state-action pairs, i.e. what action should I take in what state. We call this Q(s,a). • Given Q(s,a) it is now trivial to execute the optimal policy, without knowing r(s,a) and delta(s,a). We have: € V*(s)← maxar(s,a) +γV*(δ(s,a))[ ]Bellman Equation:Example II Check thatQ-Learning • This still depends on r(s,a) and delta(s,a). • However, imagine the robot is exploring its environment, trying new actions as it goes. • At every step it receives some reward “r”, and it observes the environment change into a new state s’ for action a. How can we use these observations, (s,a,s’,r) to learn a model? s’=st+1Q-Learning • This equation continually makes an estimate at state s consistent with the estimate s’, one step in the future: temporal difference (TD) learning. • Note that s’ is closer to goal, and hence more “reliable”, but still an estimate itself. • Updating estimates based on other estimates is called bootstrapping. • We do an update after each state-action pair. Ie, we are learning online! • We are learning useful things about explored state-action pairs. These are typically most useful because they are likely to be encountered again. • Under suitable conditions, these updates can actually be proved to converge to the real answer. s’=st+1Example Q-Learning Q-learning propagates Q-estimates 1-step backwardsExploration / Exploitation • It is very important that the agent does not simply follow the current policy when learning Q. (off-policy learning).The reason is that you may get stuck in a suboptimal solution. I.e. there may be other solutions out there that you have never seen. • Hence it is good to try new things so now and then, e.g. If T large lots of exploring, if T small follow current policy. One can decrease T over time.Improvements • One can trade-off memory and computation by cashing (s,s’,r) for observed transitions. After a while, as Q(s’,a’) has changed, you can “replay” the update: • One can actively search for state-action pairs for which Q(s,a) is expected to change a lot (prioritized sweeping). • One can do updates along the sampled path much further back than just one step ( learning).Extensions • To deal with stochastic environments, we need to maximize expected future discounted reward: • Often the state space is too large to deal with all states. In this case we need to learn a function: • Neural network with back-propagation have been quite successful. • For instance, TD-Gammon is a back-gammon program that plays at expert level. state-space very large, trained by playing against itself, uses NN to approximate value function, uses TD(lambda) for learning.Conclusion • Reinforcement learning addresses a very broad and relevant question: How can we learn to survive in our environment? • We have looked at Q-learning, which simply learns from experience. No model of the world is needed. • We made simplifying assumptions: e.g. state of the world only depends on last state and action. This is the Markov assumption. The model is called