From Reflex to Reason

Rich SuttonAT&T Labs

with thanks to Satinder Singh, Doina Precup, and Andy Barto

Overall Goal

A computational understanding of a broad span of the mind’s activities

what it computeswhy it computes it

At a high level, withoutspecifics of sensory and motor systemsspecific representations and algorithmsneural implementationslanguage

What does the mind do?Is there an overall, simple answer?

Marr’s 3 levels

Main Claims

• Mind is about predictions– making predictions– discovering what predictions can be made

• Knowledge is predictions– action-contingent and temporally-flexible predictions– agent-centric, grounded in experience from the bottom

up

• The mind’s ultimate goal is to make reward-maximizing decisions– but most of its effort is devoted to subgoal of prediction

• A few simple mechanisms enable working flexibly with predictions– TD learning and Bellman backups

Prediction Semantics

Prediction Semantics

• A prediction is a signal with meaning

• Knowing that one signal is a prediction of another enables it to do useful work for you

• When something new predicts X, you know what to do

• Prediction semantics constrains in two directions

Pred.of X

ResponseY

X

existinglink

newlink

Outline/Steps

• Reflexes and their conditioning

• Learning to get reward

• Planning, by mental simulation

• Knowledge, as temporally flexible predictions

• Reason, as flexible use of knowledge

These together are much of what the mind doesCan we explain them all in a uniform way?

Pavlovian Conditioning,the Conditioning of Reflexes

CS Tone

Eyeshock

Eyeblinkbefore learning

Eyeblinkafter learning

US

UR

CR

Almost any reflex can be conditioned:

salivationorientingheart rate, blood pressuregill withdrawallnausea, taste aversionfear, secondary reinforcersCER: freezing, suppressionneutral stimuli

• Animal can be viewed as learning that the CS predicts the US

• And then responding in anticipation

• But Why? Why should a prediction of the US produce the same response as the US?

(No US)

(Inadequate) Comp. Theories of CC• Instrumental theories -- the CR makes the US feel

better– Works well for eyeblink, salivation, not for 2ndary

reinforcers– Does not explain the similarity of CR and UR– Does not explain apparent conflict of CC and instrumental

• Anticipation theories -- whatever you are going to do, CC causes you to do it earlier– Why earlier? Earlier is not always better!– How much earlier? CR tends to occur at time of US

• Prediction theories -- CC is learning to predict the US– Works for fear, CER, 2ndary reinforcers– Does not explain response to CR or to UR– Explains “What” but not “Why”

Pred Rep’n Theory of Conditioning

The reflex is not US Response:

US Rreflex

CS learnableNOT OR

US Rreflex

CS

learnable

But Prediction of US Response:

Predof US

Rreflex

CS learnable

USlearnable

+USs couldhabituate!

Pred Rep’n Theory of Conditioning (2)

• Consider an innate, learnable association US Response– represents an innate guess, e.g., that a shock now is good

predictor of a shock coming up– but could be wrong– Predicts URs could habituate, change over time depending

on their relationship to themselves

US

supervisory

cue

CS

CS

1

2

+ prediction ofsupervisory US Response

Long USs predict themselves

Short USs are poor self-predictors

*

*

*

*

Pred Rep’n Theory of Conditioning (3)

• Implications for response topography/generation– predicts maximal CR at time of US onset (correct)– predicts CR onset only so early as to enable this– predicts threshold phenomena in CR production– predicts interaction of threshold with relative

effectiveness of reinforced and unreinforced trials

US

CR

responsetopography

Outline/Steps

• Reflexes and their conditioning

• Learning to get reward

• Planning, by mental simulation

• Knowledge, as temporally flexible predictions

• Reason, as flexible use of knowledge

The Reward Hypothesis

• Is this reasonable?• Is it demeaning?• Is there no other choice?

• It seems to be adequate and perhaps completely satisfactory

That purposes can be adequately represented as

maximization of the cumulative sum of a scalar reward signal received from the

environment

Reinforcement Learning Theory:

What to Compute and Why• Policies: States Pr(Actions)

• Value Functions

V

(s) E t 1rewardt

t1

start in s0 , follow

V : States→ ℜ

• 1-Step Models

P st+1 st ,at E rt+1 st ,at

s

Predictions!

Honeybee Brain & VUM Neuron

Hammer, Menzel

The Acrobot Problem

e.g., Dejong & Spong, 1994

Sutton, 1995

Minimum–Time–to–Goal:

4 state variables: 2 joint angles 2 angular velocities

CMAC of 48 layers

RL same as Mountain Car

1

Goal: Raise tip above line

Torqueapplied

here

tip

Reward = -1 per time step

fixed base

Prediction Semantics of RL

Value, a pred. of reward

reward

fixedlink

Action SelectionPick the highestvalued action

Representationsof state

and action

learnedlinks

An action that predicts reward in a state...should to that extent be favored in that state

Examples of Reinforcement Learning• Robocup Soccer Teams Stone & Veloso, Reidmiller et al.

– World’s best player of simulated soccer, 1999; Runner-up 2000

• Inventory Management Van Roy, Bertsekas, Lee & Tsitsiklis– 10-15% improvement over industry standard methods

• Dynamic Channel Assignment Singh & Bertsekas, Nie & Haykin– World's best assigner of radio channels to mobile telephone calls

• Elevator Control Crites & Barto– (Probably) world's best down-peak elevator controller

• Many Robots– navigation, bi-pedal walking, grasping, switching between skills...

• TD-Gammon and Jellyfish Tesauro, Dahl– World's best backgammon player

TD-Gammon

. . .. . .

. . .. . .

Value

TD Error

Vt+1 Vt

Action selectionby 2-3 ply search

Tesauro, 1992-1995

Start with a random Network

Play millions of games against itself

Learn a value function from this simulated experience

This produces arguably the best player in the world

Prediction Semantics in TD-Gammon

• A prediction of winning can substitute for winning– the central idea of Temporal-Difference (TD) learning

• learning a prediction from a prediction!

– also key idea of dynamic programming– and all heuristic search

• In lookahead search, predictions are composed to produce longer-term predictions– key to all state-space planning– suggests prediction semantics is key element of

reasoning

Outline/Steps

• Reflexes and their conditioning

• Learning to get reward

• Planning, by mental simulation

• Knowledge, as temporally flexible predictions

• Reason, as flexible use of knowledge

Planning as RL over Mental Simulation

1. Learn a model of the world’s transition dynamicstransition probabilities, expected immediate rewards“1-step model” of the world

2. Use model to generate imaginary experiencesinternal thought trials, mental simulation (Craik, 1943)

3. Apply RL as if experience had really happened

Reward

ValueFunction

1-Step Model

Policy

I.e., learning on model-generated experience:

Dyna Algorithm

1. s current state

2. Choose an action, a, and take it

3. Receive next state, s’, and reward, r4. Apply RL backup to s, a, s’, r

e.g., Q-learning update

5. Update Model(s, a) with s’, r6. Repeat k times:

- select a previously seen state-action pair s,a

- s’, r Model(s, a)

- Apply RL backup to s, a, s’, r7. Go to 1

value/policy

model experience

acting

modellearning

directRL

planning

State-Space Searchis based on a Prediction

Semanticsin seeking to evaluatethis state

we use predictions from these

Prediction Semantics in Planning

is just like in TD-Gammon

• Predictions substitute for path outcomes

• Predictions are composed to predict consequences of arbitrary sequences of action

Naïve RL Theory of Reason

Reward

ValueFunction

1-Step Model

Policy

Reason is RL on model-generated experience

• Pro:– Very simple, uniform, general– Sufficient to reproduce e.g., latent learning

• Con– Seems too low-level– Represents only a limited kind of knowledge

Outline/Steps

• Reflexes and their conditioning

• Learning to get reward

• Planning, by mental simulation

• Knowledge, as temporally flexible predictions

• Reason, as flexible use of knowledge

Experience

Agent Worldactions

observations

L at 3 ,at 2 ,at 1,at L ?

L ot 3,ot 2 ,ot 1,ot L ? ?

Actions:

Observations:

Experience is the data; it is all we really know Experience provides something for knowledge to be about

A mind interacts with its world

To produce two time series:

Experience

• The world is a black box, known only by its I/O behavior (observations in response to actions)

• Therefore, all meaningful statements about the world are statements about the observations it generates

• The only observations worth talking about are future ones

The only meaningful things to say about the world are predictions

World Knowledge Predictions

Therefore:

Predictions = statements about the joint distribution of future observations and actions

Non-predictive “Knowledge”• Mathematical knowledge, theorems and proofs

– always true, but tell us nothing about the world– not world knowledge

• Uninterpretted signals, e.g., useful representations– real and useful, but not by themselves world

knowledge, only an aid to acquiring it

• Knowledge of the past• Policies

– could be viewed as predictions of value– but by themselves are more like uninterpretted

signals

Predictions capture “regular”, descriptive world knowledge

Every Prediction must be Grounded

in Two Directions

if I do action 1, then obs 12 will be 0

for three steps

history ofactions &

observations

recognition grounding

prediction

prediction grounding

“symbol grounding”

“prediction semantics”

Both Recognition and Prediction Grounding are Needed

• “Classical” AI systems omit recognition grounding– e.g., “Tweety is a bird”, “John loves Mary”– sometimes called the “symbol grounding problem”

• Modern AI sytems tend to skimp prediction grounding– supervised learning, Bayes nets, robotics…

• It is not OK to leave prediction grounding to external, human observers– the information is just not in the machine– we don’t understand it; we haven’t done our job!

• Yet this is such an appealing shortcut that we have almost always done it

Prediction Semantics formalized as Macros-Actions

Let : States Pr(Actions) be an arbitrary policyLet : States Pr({0,1}) be a termination condition

Then macro-action <,> is a kind of experiment – do until says “stop” – measure something about the resulting experienceSuppose we measure – the state at the end of the experiment – the total reward during the experimentThen the macro prediction for <,> would predict Pr(end-state), E{total reward} given start-state

Predictions of this form can represent a lot... ...possibly all world knowledge

Sutton, Precup & SinghAIJ 1999 etal.

Rooms Example

o2

HALLWAYS

o1

up

down

rightleft

(to each room's 2 hallways)

G2

Fail 33% of the time

G1

TargetHallway

Policy of one macro-action:

Sutton, Precup,& Singh, 1999

8 multi-step macro-actions

4 stochasticprimitive actions

Planning with Macro-Predictions

Iteration #0 Iteration #1 Iteration #2

with cell-to-cellprimitive actions

Iteration #0 Iteration #1 Iteration #2

with room-to-roomoptions

V(goa l)=1

V (goa l)=1

macro-actions

Learning Path-to-Goal with and without Hallway Macros-Actions

Episodes

Stepsper

episode

1 10 100 1000 10,00010

100

1000

Actions

Macros

Macros& actions

Illustration: Reconnaissance Mission Planning (Problem)

• Mission: Fly over (observe) most valuable sites and return to base

• Stochastic weather affects observability (cloudy or clear) of sites

• Limited fuel• Intractable with classical optimal

control methods• Temporal scales:

– Actions: which direction to fly now

– Options: which site to head for • Options compress space and time

– Reduce steps from ~600 to ~6– Reduce states from ~1011 to ~106

QO

* (s, o) =rso + ps ′s

o VO* ( ′s )

′s∑

any state (106) sites only (6)

10

50

50

50

100

25

15 (reward)

5

25

8

Base100 decision steps

options

(mean time between weather changes)

30

40

50

60

Illustration: Reconnaissance Mission Planning (Results)

• SMDP planner:– Assumes options followed to

completion– Plans optimal SMDP solution

• SMDP planner with re-evaluation– Plans as if options must be

followed to completion– But actually takes them for

only one step– Re-picks a new option on

every step• Static planner:

– Assumes weather will not change

– Plans optimal tour among clear sites

– Re-plans whenever weather changes

Low FuelHigh Fuel

Expected Reward/Mission

SMDPPlanner

StaticRe-planner

SMDP planner

with re-evaluation of options on

each step

Temporal abstraction finds better approximation than static planner, with little more computation than SMDP planner

Outline/Steps

• Reflexes and their conditioning

• Learning to get reward

• Planning, by mental simulation

• Knowledge, as temporally flexible predictions

• Reason, as flexible use of knowledge

Reason

Combining knowledge to obtain new knowledge,flexibly and generally

We must be able to reason about any event as a possible (sub)goal, not just about rewards

This is the final step

Subgoals

• Many natural macro-actions are goal-oriented– E.g., drive-to-work, open-the-door

• So replicate planning in-miniature for each subgoal• Macros can then be learned to achieve each

subgoal• Many can be learned at once, independently

– Solves classic problem of subgoal credit assignment– Solves psychological puzzle of goal-oriented action

• Models of such macros are goal-oriented recognizers– correspond to classical “concepts”– e.g., a “chair” state is one where sitting is predicted to

work

rooms exampl

e

Rooms ExampleIndependent learning of all 8

Subgoals

Time steps

RMS Error insubgoal values

Two subgoalstate values

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 20,000 40,000

Time Steps60,000

upperhallwaysubgoal

learnedvalues

idealvalues

lowerhallwaysubgoal

80,000 100,0000

0.1

0.2

0.3

0.4

0 20,000 40,000 60,000 80,000 100,000

All 8 hallway macros and predictions are learned accurately and efficiently while actions are selected totally at random

Co-Existence of Hedonism and Exploration/Constructivism

• The ultimate goal is still reward• Still one primary policy and set of values• But many other policies, values, and predictions

are learned not directly in service of reward• Most time is spent in exploration and discovery, gaining knowledge rather than reward:

– What possibilities does the world afford?– How can I control and predict it in a variety of ways?– What concepts can be learned that might help later?

• From hedonism to curiosity and constructivism

Main Claims

• Mind is about predictions– making predictions– discovering what predictions can be made

• Knowledge is predictions– action-contingent and temporally-flexible predictions– agent-centric, grounded in experience from the bottom

up

• The mind’s ultimate goal is to make reward-maximizing decisions– but most of its effort is devoted to subgoal of prediction

• A few simple mechanisms enable working flexibly with predictions– TD learning and Bellman backups

Prediction Semantics

What is New?

• The formalization of macro-actions

– provide temporal abstraction

– as well as action contingency (experiments)

– mesh seemlessly with learning and planning methods

• Using the goal-oriented machinery of RL

– for knowledge construction

– for perceptual concepts

• Taking the discipline of predictive knowledge seriously

– speaking only in terms of the subjective, experiential data

Should Knowledge be Experiential?

Allowing only Predictions in terms of Data? loses

• Expressiveness– can’t talk about objects, space, people; no “is-a” or “part-

of”

• External (human) coherence– verbal labels, interpretability, explainability, calibration– the “shortcut” of entering knowledge directly into the

agent

gains • The knowledge will have meaning to the machine• It can be mechanically learned/verified/extended • It will be suited for a general reasoning processes

– composition and backup of predictions to yield new predictions