Fair and Sustainable Resource Allocation in Self-Organising - - PowerPoint PPT Presentation

Fair and Sustainable Resource Allocation in Self-Organising Multi-Agent Systems

Jeremy Pitt

Department of Electrical and Electronic Engineering

Journ´ ees Francophones sur les Syst` emes Multi-Agents (JFSMA) Plate-forme Intelligence Artificielle (PFIA) Rennes, 29/06–1/07 2015

Agenda

Context: resource allocation in open multi-agent systems Problem: how to ensure that allocation is fair and sustainable Sustainability: formalisation of Elinor Ostrom’s institutional design principles for self-governing institutions Fairness: formalisation of Nicholas Rescher’s theory of distributive justice based on legitimate claims Computational justice in ‘technical’ and ‘socio-technical’ systems Summary and conclusions

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Context

Open multi-agent systems

◮ autonomous, heterogeneous, (possibly) competing components

(agents)

‘Technical’ systems – composed of purely computing agents

◮ Grid computing, cloud computing, . . . ◮ Ad hoc networks, sensor networks, vehicular networks, . . . ◮ Virtual organisations, . . . ◮ Reconfigurable manufacturing, evolvable manufacturing, . . . ◮ Power systems, . . .

Common requirement: a collective action situation in which the agents (aka appropriators) have to collectivise and distribute resources, in the context of . . .

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. . . Key Features of Open Systems

Self-determination (no centralised ‘authority’)

◮ Selection and modification of the rules for resource allocation

are determined by the agents themselves

Expectation of error and corrective action

◮ Sub-ideal behaviour is to be expected (by accident, necessity

• r malice (free-riding)), the enforcement of sanctions for

non-compliance and/or restoration of compliant states

Economy of scarcity

◮ Sufficient resources to keep agents satisfied at the long-term,

but insufficient to meet all demands at a particular time-point

Endogeneous resources

◮ Computing a resource allocation must be ‘paid for’ from the

same resources being allocated

No full disclosure

◮ Agents are autonomous and their internal states cannot be

checked

Jeremy Pitt Fair and Sustainable Resource Allocation in Self-Organising Multi-Agent Systems 4 / 22

Methodology

Introspection – ask: how do people solve this sort of problem? Aside – with the intention of applying the sociologically-inspired computing methodology

Pre-formal Theory Calculus1 ... Calculusn Computer Model Observed Phenomena Observed Perfomance

Expressive capacity Requirements coverage ⇐ ⇒ Conceptual granularity Computational tractability ⇐ ⇒ Consistency Usability

formal characterisation principled operationalisation theory construction controlled experimentation

◮ Communication – speech act theory ◮ Socialisation – trust, forgiveness and social networks ◮ Organisation and Deliberation – norms and rules of order

Answer: evolve institutions for self-governing common-pool resource management

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Common-Pool Resource Management

People are very good at “making stuff up” In particular, making up and writing down conventional rules to (voluntarily) regulate/organise their own behaviour Elinor Ostrom (Nobel Laureate for Economic Science, 2009)

Common-pool resource (CPR) management by self-governing institutions Avoidance (not refutation) of ‘the tragedy of the commons’, and ‘zero contribution’ thesis Alternative to privatisation or centralisation

Role-based protocols for implementing conventional procedures Self-organisation: change the rules according to other (‘fixed’, ‘pre-defined’) sets of rules Self-determination: those affected by the rules participate in their selection

Jeremy Pitt Fair and Sustainable Resource Allocation in Self-Organising Multi-Agent Systems 6 / 22

Self-Governing the Commons with Institutions

Definition: “set of working rules that are used to determine who is eligible to make decisions in some arena, what actions are allowed or constrained, ... [and] contain prescriptions that forbid, permit or require some action or outcome” [Ostrom] Conventionally agreed, mutually understood, monitored and enforced, mutable and nested Nesting: tripartite analysis

• perational-, collective- and constitutional-choice rules

Decision arenas [Action Situations]

Requires representation of Institutionalised Power

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Sustainability of the Commons

Analysis: necessary conditions for successful enduring institutions ‘Supply’: handbook of institutional design principles

P1 Clearly defined boundaries P2 Congruence between appropriation and provision rules and the state of the prevailing local environment P3 Collective choice arrangements P4 Monitoring by appointed agencies P5 Flexible scale of graduated sanctions P6 Access to fast, cheap conflict resolution mechanisms P7 Minimal recognition by external authorities of the right to self-organise P8 Systems of systems

Apply the methodology to Ostrom’s principles

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Self-Organising Electronic Institutions (SOEI)

Electronic Institutions

Formalise structural, functional and procedural aspects of institutions in mathematical or computational form Self-Organising: selection and modification of structures, functions, and procedures are determined by the members

inc rep 1 1

1 2 3 4 4’ 5

a b b a a b b ∼ a A DG A = DG A DG A DG A DG A DG

scr3 scr2 scr1 scr4

• cr2

wdMethod DG1 W raMethod DG1 wdMethod DG3 DG2 {v(·)}a2DG3 {v(·)}a2DG2 {v(·)}a2DG1 {v(·)}a∈DG1 W {da(·)}a2A {ra(·)}a2A

Self-Organising electronic institutions represented in framework of dynamic norm-governed systems (Artikis, 2012)

SOEI encapsulating Ostrom’s institutional design principles can be axiomatised in computational logic using the Event Calculus, and directly executed Experiments showed that the more principles that were axiomatised, it was more likely that the institution could maintain ‘high’ levels of membership and sustain the resource

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“That’s Not Fair” – Distributive Justice and CPRs

Is the axiomatisation of the allocation method, and the

• utcomes it produces, ‘fair’, now, (with respect to) the past,

and in the future? What fairness criteria to use to distribute the resources?

Egalitarian: maximise satisfaction of most disadvantaged agent Envy-free: no agent prefers the allocation of any other agent Proportional: all agents receive the same share Equitable: each agent derives the same utility . . .

There are many objective metrics for measuring ‘fairness’

• utcomes

Limitations of existing fairness criteria:

Many not appropriate under an economy of scarcity Focus on a single aspect (monistic) Often disregard temporal aspects (e.g. repeated allocations)

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Experimental Setting – Linear Public Good Game (LPG)

LPG commonly used to study free-riding in collective action situations Variant game: LPG ′ – in each round, each agent:

Determines the resources it has available, gi ∈ [0, 1] Determines its need for resources, qi ∈ [0, 1]

In an economy of scarcity, qi > gi

Makes a demand for resources, di ∈ [0, 1] Makes a provision of resources, pi ∈ [0, 1] (pi ≤ gi) Receives an allocation of resources, ri ∈ [0, 1] Makes an appropriation of resources, r ′

i ∈ [0, 1]

Agents may not comply, r ′

i > ri

Utility in LPG ′: accrued resources Ri = r′

i + (gi − pi)

Ui = aqi + b(Ri − qi), if Ri ≥ qi aRi − c(qi − Ri),

• therwise

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Rescher’s Legitimate Claims

Canons of distributive justice: treat people according to . . .

. . . as equals . . . needs . . . actual productive contribution . . . efforts and sacrifices “ . . . a valuation of their socially-useful services . . . supply and demand . . . ability, merit or achievements

Each canon, taken in isolation, is inadequate to achieve ‘fairness’ Distributive justice consists of evaluating and prioritising agents legitimate claims, both positive and negative Determine what the legitimate claims are, how they are accommodated in case of plurality, and how they are reconciled in case of conflict

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Representation of Legitimate Claims in LPG ′

Equals

Average allocation

T

t=0 ri(t)

T

Allocation frequency

T

t=0(ri(t)>0)

T

Needs

Average demands

T

t=0 di(t)

T

Contribution

Average provision

T

t=0 pi(t)

T

Effort

Number of rounds present |{t|member(i, C, t) = true}|

Social utility

Time as head |{t|roles(i, C, t) ∋ head}|

Supply & demand

Compliance |{t|r ′

i (t) = ri(t)}|

Ability, merits...

n/a

di (t) Demand of ... ...agent i at time t pi (t) Provision of ... ri (t) Allocation to ... r′

i (t)

Appropriation of ... member(i, C, t) i is a member of C at time t ... roles(i, C, t)(i, C, t) head is in the set of roles occupied by i in C at time t ... Jeremy Pitt Fair and Sustainable Resource Allocation in Self-Organising Multi-Agent Systems 13 / 22

Accommodation in Case of Plurality

Each canon Ci treated as a voter in a Borda count protocol,

• n agents

It ranks agents according to some features (e.g. needs, contribution...) It assigns a score to each agent, Bi(a)

To combine claims, a weight wi is attached to each canon Final Borda score of agent a is: B(a) =

n

• i=1

wi · Bi(a) Use final Borda ranking as a queue to allocate resources Allocate agents’ full requests until no more resources available

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Reconciliation in Case of Conflict

Instead of fixing the weights of each canon, allow the agents to modify them At the end of each round

Agents vote for the canons in order of preference (according to rank given by each canon) using a modified Borda count∗ Borda score computed for each canon Canons with better than average Borda score have weight increased, otherwise decreased

This supports Ostrom’s Principle 3: “those affected by the

• perational-choice rules participate in the selection and

modification of those rules”

∗Allowing for some candidates having the same number of points Jeremy Pitt Fair and Sustainable Resource Allocation in Self-Organising Multi-Agent Systems 15 / 22

Some results

Compare self-organising legitimate claims, fixed weights, random and ration allocation methods Self-organising legitimate claims...

... was the only method producing endurance of the system and benefiting compliant agents ... was the fairest† method (wrt to ration and fixed LC) ... was preferred by the compliant agents ... leads to a very fair overall allocation in spite of a series of rather unfair allocations

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 20 40 60 80 100 Gini index Round Step Accumulated †Using Gini inequality index over accumulated allocations to measure fairness Jeremy Pitt Fair and Sustainable Resource Allocation in Self-Organising Multi-Agent Systems 16 / 22

Ramifications

Cost of monitoring and enforcement

Monitoring is not free In a system with endogenous resources, the cost of monitoring has to be ‘paid for’ from the very same resources that are to be allocated It is as easy to deplete an endogenous resource by

• ver-monitoring as under-

Unrestricted self-modification

Suber’s Thesis: any system that allows unrestricted self-modification of its rules inevitably ends in paradox of self-amendment, incompleteness or inconsistency

Computational justice

Ensuring the correctness of algorithmic deliberation and decision-making Multi-faceted: social —, distributive —, retributive —, procedural — and interactional justice

What happens when these mechanisms are injected back into the society which inspired them ⇒ socio-technical systems?

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What is Computational Justice?

Computational justice lies at the intersection of Computer Science and Economics, Philosophy, Psychology and Jurisprudence It is primarily concerned with establishing some aspect of ‘correctness’ in the outcomes of algorithmic decision-making and deliberation It comprises... ... formal and/or computational models of judicial processes and systems ... representation, organisation and administration of rules or policies ... importing concepts from the Social Sciences into computing applications ... exporting some ideas back to socio-technical systems

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Forms of Justice (that we consider)

Natural justice

◮ do agents participate in the decision making affecting them?

Distributive justice

◮ how to fairly distribute resources?

Retributive justice

◮ how to punish non-compliant behaviour?

Procedural justice

◮ is a procedure fit-for-purpose? is it engaging/open/efficient?

Interactional justice

◮ how fairly are the agents treated by decision makers?

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Key features and justice

Self-determination Key features Expectation of error Enforcement Economy of scarcity Endogeneous resources No full disclosure Natural Justice Retributive Distributive Procedural Interactional

participation, inclusion, voting

(1)

sanctions, appeals

(2)

fair allocation

(3)

efficiency

(4)

information, justification

Jeremy Pitt Fair and Sustainable Resource Allocation in Self-Organising Multi-Agent Systems 20 / 22 (1) Pitt et al, The Axiomatisation of Socio-Economic Principles for Self-Organising Systems, SASO 2011 (2) , Provision and appropriation of common-pool resources without full disclosure, PRIMA 2012 (3) , Self-organising common-pool resource allocation and canons of distributive justice, SASO 2012 (4) , Procedural Justice and ‘Fitness-for-Purpose’ . . ., PRIMA 2013

Summary and Conclusions

Original problem – fair and sustainable resource allocation in

• pen multi-agent systems

Formal model of Ostrom’s institutional design principles Formal model of Rescher’s theory of distributive justice

Inject these ideas back into socio-technical systems

(Towards) Formal models of collective awareness, social capital, and computational justice

We end up with alternative approach to smart(er) cities If the only solution you have is an Ostrom-shaped hammer, then every problem you face is a collective action-shaped nail

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Acknowledgements

UK EPSRC and EU for funding Many people for collaborations etc.

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