On Linking Reinforcement Learning with Unsupervised Learning Cornelius Weber FIGSS talk, FIAS, 20 th April 2009

for taking action, we need only the relevant features x y z

unsupervised learning in cortex reinforcement learning in basal ganglia state space actor Doya, 1999

reinforcement learning go up? go right? go down? go left?

reinforcement learning input s action a weights

action a reinforcement learning minimizing value estimation error: d v(s,a) ≈ 0.9 v(s’,a’) - v(s,a)‏ d v(s,a) ≈ 1 - v(s,a)‏ moving target value fixed at goal v(s,a) value of a state-action pair (coded in the weights)‏ repeated running to goal: in state s, agent performs best action a (with random), yielding s’ and a’ --> values and action choices converge input s weights

actor go right? go left? can’t handle this! simple input go right! complex input reinforcement learning input (state space)‏

sensory input reward action complex input scenario: bars controlled by actions, ‘up’, ‘down’, ‘left’, ‘right’; reward given if horizontal bar at specific position

need another layer(s) to pre-process complex data feature detection action selection network definition: s = softmax(W I)‏ P(a=1) = softmax(Q s)‏ v = a Q s a action s state I input Q weight matrix W weight matrix position of relevant bar encodes v feature detector

feature detection action selection network training: E = (0.9 v(s’,a’) - v(s,a)) 2 = δ 2 d Q ≈ dE/dQ = δ a s d W ≈ dE/dW = δ Q s I + ε a action s state I input W weight matrix minimize error w.r.t. current target reinforcement learning δ-modulated unsupervised learning Q weight matrix

note: non-negativity constraint on weights network training: minimize error w.r.t. target V π identities used:

SARSA with WTA input layer

RL action weights feature weights data learning the ‘short bars’ data reward action

short bars in 12x12 average # of steps to goal: 11

RL action weights feature weights input reward 2 actions (not shown)‏ data learning ‘long bars’ data

WTA non-negative weights SoftMax non-negative weights SoftMax no weight constraints

models’ background: - gradient descent methods generalize RL to several layers Sutton&Barto RL book (1998); Tesauro (1992;1995) - reward-modulated Hebb Triesch, Neur Comp 19, (2007), Roelfsema & Ooyen, Neur Comp 17, (2005); Franz & Triesch, ICDL (2007)‏ - reward-modulated activity leads to input selection Nakahara, Neur Comp 14, (2002) - reward-modulated STDP Izhikevich, Cereb Cortex 17, (2007), Florian, Neur Comp 19/6, (2007); Farries & Fairhall, Neurophysiol 98, (2007);... - RL models learn partitioning of input space e.g. McCallum, PhD Thesis, Rochester, NY, USA (1996)‏

Discussion - two-layer SARSA RL performs gradient descent on value estimation error - approximation with winner-take-all leads to local rule with δ-feedback - learns only action-relevant features - non-negative coding aids feature extraction - link between unsupervised- and reinforcement learning - demonstration with more realistic data still needed Bernstein Focus Neurotechnology, BMBF grant 01GQ0840 EU project “IM-CLeVeR”, call FP7-ICT Frankfurt Institute for Advanced Studies, FIAS Sponsors

Bernstein Focus Neurotechnology, BMBF grant 01GQ0840 EU project “IM-CLeVeR”, call FP7-ICT Frankfurt Institute for Advanced Studies, FIAS Sponsors thank you...