Zhai Yuqing

yqzhai@seu.edu.cn

Learning in Multi-agent System

Outline

• Agent Learning

• Multi-agent learning

• Reinforcement Learning & Multi-agent Reinforcement Learning

Agent Learning

Why Learning?

• Learning is essential for unknown environments,– i.e., when designer lacks omniscience

• Learning is useful as a system construction method,– i.e., expose the agent to reality rather than trying to

write it down

• Learning modifies the agent's decision mechanisms to improve performance

Why Learning?• It is difficult to hand-design behaviours that act optimally (or

even close to it)

• Agents can optimize themselves using reinforcement learning

– Not learning new concepts (or behaviours), but given a set of states and actions it can find best policy

– Is this just adaptive control?

• Learning can be done on-line and continuously throughout lifetime of agent, adapting to (slowly) changing situations

Learning

Policy

World,

State

Learning Algorithm

Actions

Observations,Sensations

Rewards

Learning to act in the world

Policy

Environ-ment

Learning Algorithm

Actions

Observations,Sensations

Rewards

Other agents(possibly learning)

?

World

Learning Agent Architecture

• A learning agent can be thought of as containing a performance element that decides what actions to take and a learning element that modifies the performance element so that it makes better decisions

Learning Agent Architecture

Multi-agent Learning

Learning in Multiagent Systems

• Intersection of DAI and ML

• Why bring them together?– There is a strong need to equip Multiagent

systems with learning abilities– The extended view of ML as Multiagent

learning is qualitatively different from traditional ML and can lead to novel ML techniques and algorithms

Multi-Agent Learning Problem:

• Agent tries to solve its learning problem, while other agents in the environment also are trying to solve their own learning problems. challenging non-stationarity.

• Main scenarios: (1) cooperative; (2) self-interest (many deep issues swept under the rug)

• Agent may know very little about other agents:– payoffs may be unknown– learning algorithms unknown

• Traditional method of solution: game theory (uses several questionable assumptions)

Multi-agent Learning Problem• Agent tries to solve its own learning problem, while other agents in the

environment try to solve their own learning problems

• Larger state space– Might have to include state of other robots in own state

• Problems of Multi-Agent RL– All of problems from single agent– Other agents unpredictable or non-stationary– Should reinforcement be local or global?– Was robot trying to achieve goal or reacting to other robots when

doing a good action?

Learning in Multi-Agent Systems• No Doubt learning is of great importance for MAS !• Challenge:

– Multi-Agent learning problem. The optimal policy changes. Other agents are learning too.

– Can we have a unifying framework in which this learning can be understood.

• Challenging MAS-domains:– Robotic soccer– Traffic– Robotic rescue– Trading agents, e-commerce– Automated Driving

General Characterization

• Principal categories of learning

• The features in which learning approaches may differ

• The fundamental learning problem known as the credit-assignment problem

Principal Categories

• Centralized Learning (isolated learning)– Learning executed by a single agent, no

interaction with other agents– Several centralized learners may try to obtain

different or identical goals at the same time

Principal Categories

• Decentralized Learning (interactive learning)– Several agents are engaged in the samesame learning process

– Several groups of agents may try to obtain different or identical learning goals at the same time

• Single agent may be involved in several centralized/decentralized learning processes at the same time

Learning and Activity Coordination

• Previous research on coordination focused on off-line design of behavioral rules, negotiation protocols, etc…

• Agents operating in open, dynamic environments must be able to adapt to changing demands and opportunities

• How can agents learn to appropriately coordinate their activities?

Learning about and from Other Agents

• Agents learn to improve their individual performance

• Better capitalize on available opportunities by prediction the behavior of other agents (preferences, strategies, intentions, etc…)

Learning Organizational Roles

• Assume agents have the capability of playing one of several roles in a situation

• Agents need to learn role assignments to effectively complement each other

Learning Organizational Roles

• The framework includes Utility, Probability and Cost (UPC) estimates of a role adopted at a particular situation– UtilityUtility – desired final state’s worth if the agent adopted

the given role in the current situation

– ProbabilityProbability – likelihood of reaching a successful final state (given role/situation)

– CostCost – associated computational cost incurred

– PotentialPotential – usefulness of a role in discovering pertinent global information

Learning Organizational Roles:Theoretical Framework

• sets of situations and roles for agent k• An agent maintains vectors of UPC

• During the learning phase:

• rates a role by combining the component

measures

kk RS ,

kk RS

kRj jsjsjsjs

rsrsrsrs

PotentialCPUf

PotentialCPUfr

),,,(

),,,()Pr(

f

Learning Organizational Roles:Theoretical Framework

• After the learning phase is over, the role to be played in situation s is:

• UPC values are learned using reinforcement learning

• UPC estimates after n updates:

),,,(maxarg jsjsjsjsRj

PotentialCPUfrk

nrs

nrs

nrs otentialPPU ˆ,ˆ,ˆ

Learning Organizational Roles:Updating the Utility

• S – the situations encountered between the time of adopting role r in situation s and reaching a final state F with utility

• The utility values for all roles chosen in each of the situation in S are updated:

FU

Fnrs

nrs UUU ˆ)1(ˆ 1

Learning Organizational Roles:Updating the Probability

• - returns 1 if the given state is successful

• The update rule for probability: )(ˆ)1(ˆ 1 FOPP n

rsn

rs

]1,0[: SO

Learning Organizational Roles:Updating the Potential

• - returns 1 if in the path to the final state, conflicts are detected and resolved by information exchange

• The update rule for potential: )(ˆ)1(ˆ 1 SConfotentialPotentialP n

rsnrs

)(SConf

Learning to Exploit an Opponent:Model-Based Approach

• The most prominent approach in AI for developing playing strategies is the minimaxminimax algorithm– Assumes that the opponent will choose the

worst move

• An accurate model of the opponent can be used to develop better strategies

Learning to Exploit an OpponentModel-Based Approach

• The main problem of RL is its slow convergence

• Model based approach tries to reduce the number of interaction examples needed for learning

• Perform deeper analysis of past interaction experience

Model Based Approach

• The learning process is split into two separate stages:– Infer a model of the other agent based on past

experience– Utilize the learned model for designing

effective interaction strategy for the future

Reducing Communication by Learning

• Learning is a method for reducing the load of communication among agents

• Consider the contract-net approach:– Broadcasting of task announcement is assumed– Scalability problems when the number of

managers/tasks increases

Reducing Communication in Contract-Net

• A flexible learning-based mechanism called addressee learningaddressee learning

• Enable agents to acquire knowledge about the other agents’ task solving abilities

• Tasks may be assigned more directly

Reducing Communication in Contract-Net

• Case-based reasoning is used for knowledge acquisition and refinement

• Humans often solve problems using solutions that worked well for similar problems

• Construct cases – problem-solution pairs

Case-Based Reasoning in Contract Net

• Each agent maintains it own case base

• A case consists of:– Task specification– Info about which agent already solved the task

and the quality of the solution

• Need a similarity measure for tasks

ii imimiii VAVAT ,...,11

Case-Based Reasoning in Contract Net

• Distance between two attributes is domain-specific

• Similarity between two tasks and :

• For task a set of similar tasks is:

),( jsir AADist

iT jT

r s

jsirji AADistTTSimilar ),(),(

iT

85.0),(:)( jiji TTSimilarTTS

Case-Based Reasoning in Contract Net

• An agent has to assign task to another agent

• Select the most appropriate agents by computing their suitability:

iT

)(

),()(

1),(

ij TSTj

ii TAPerform

TSTASuit

Improving Learning by Communication

• Two forms of improving learning by communication are distinguished:

– Learning based on low-level communication (e.g. exchanging missing information)

– Learning based on high-level communication (e.g. mutual explanation)

Improving Learning by Communication

• Example: Predator-Prey domain– Predators are Q-learners– Each predator has a limited visual perception– Exchange sensor data – low-level

communication– Experiments show that it clearly leads to

improved learning results

Knowledge exchange in MAS

• More sophisticated implementations provide knowledge exchange capabilities – Exchange the strongest rules they have learned– Multi-agent Mutual Learning(MAML)

Some Open Questions…• What are the unique requirements and conditions for

Multiagent learning?

• Do centralized and decentralized learning qualitatively differ from each other?

• Development of theoretical foundations of decentralized learning

• Applications of Multiagent learning in complex real-world environments

Reinforcement Learning & Multi-agent Reinforcement

Learning

6

12

Reinforcement Learning Approach

Overview:

TD [Sutton 88], Q-learning [Watkins 92]• Agent can estimate a model of state transition probabilities of

E(Environment), if E has a fixed state transition probability (; E is a MDPs) .

Profit sharing [Grefensttette 88]• Agent can estimate a model of state transition probabilities of E, even

though E does not have a fixed state transition probability.

c.f. Dynamic programming • Agent needs to have a perfect model of state transition probabilities of E.

Feature: The Reward won’t be given immediately after agent’s action. Usually, it will be given only after achieving the goal. This delayed reward is the only clue to agent’s learning.

State Recognizer

Action Selector

LookUp Table

W (S, a )

Learner

Agent Input

Action

En

vironm

ent

Reward

En

vironm

ent

E

Agent

Environment

action at

rt+1

st+1

reward rtstate st

Reinforcement Learning Scenario

Example

                                                                                                                                                Q(s, ared)     =  0 +  × 81    =  72

      Q(s, agreen)  =  0 +  × 100  =  90

      Q(s, ablue)    =  0 +  × 100  =  90

Multi-agent RL

• Basic idea– Combine the learning process in an unknown environ

ment with the interactive decision process of multiple agents

– There is no single utility function to optimize

– Each agent has a different objective and its payoff is determined by the joint action of multiple agents

Challenges in Multi-agent RL

• Curse of dimensionality – The number of parameters to be learned increases dramatically

with the number of agents • Partial observability

– states and actions of the other agents which are required for an agent to make decision are not fully observable

– inter-agent communication is usually costly – Notes: Partially observable Markov decision processes (POMD

Ps) have been used to model partial observability in probabilistic AI

The Multi-Agent Reinforcement Learning (MARL) Model

• Multiple selfish agents in a stationary dynamic environment.

• Environment modeled as a Stochastic (a.k.a Markov) Game (SG or MG).

• Transition and Payoff are functions of all agents’ actions.

The MARL Model (cont.)

• Transition probabilities and payoffs are initially unknown to agent.

• Agent’s goal – maximize return.

Typical Multi-agent RL methods

• Value Iteration Learning [Sutton and Barto ]– Based on different concepts of equilibrium in game theory

• Min-max solution-based learning algorithm in zero-sum stochastic games [Littman]

• Nash Equilibrium-based learning algorithm[Wellman]– Extending Littman’s algorithm to the general-sum games

• Correlated Equilibrium based learning algorithm[Hall ]– Consider the possibility of action correlation among agents

Typical Multi-agent RL methods

• Multiple-person decision theory-based– Assume that each agent plays a best-response a

gainst stationary opponents– Require the joint action of agents to converge t

o Nash Equilibrium in self-play

– Learn quickly while losing and slowly while winning

– Learn best response when opponents are stationary, otherwise move to equilibrium

Typical Multi-agent RL methods

• Integrating RL with Coordination Learning – Joint action learner

• Independent Learner– Ignore the existence of other agents– Just apply RL in the classic sense

Typical Multi-agent RL methods

• Hierarchical Multi-agent RL– Each agent is given an initial hierarchical decompositi

on of the overall task– Define cooperative subtasks to be those subtasks in w

hich coordination among agents has significant effect on the performance of the overall task

– Cooperative subtasks are usually defined at highest level(s) of the hierarchy

MAL Foundation• The game theoretic concepts of stochastic

games and Nash equilibria• Learning algorithms use stochastic games as a na

tural extension of Markov decision processes (MDPs) to multiple agents – Equilibria learners

• Nash-Q , Minimax-Q • Friend-or-Foe-Q • gradient ascent learner

– best-response learner

Multiagent Q-learning desiderata

“performs well” vs. arbitrarily adapting other agents best-response probably impossible

Doesn’t need correct model of other agents’ learning algorithms

But modeling is fair game

Doesn’t need to know other agents’ payoffs

Estimate other agents’ strategies from observation do not assume game-theoretic play

No assumption of stationary outcome: population may never reach eqm, agents may never stop adapting

Self-play: convergence to repeated Nash would be nice but not necessary. (unreasonable to seek convergence to a one-shot Nash)

Finding Nash equilibrium

• Game theoretic approach which supposes the complete knowledge of the reward structure of the underlying game by all the agents – Each agent calculates an equilibrium, by using

mathematical programming – Suppose that the other agents are rational

Potential applications of MARL

• E-commerce – agents buying and selling over the internet.

• Autonomous computing, e.g., automatic fault recovery.

• Exploration of environments that are inaccessible to humans: bottom of oceans, space, etc…

The End