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Liquid Democracy (LD) uses transitive delegations in voting. In its simplest form, it is used for binary decisions, however its promise holds also for more advanced voting settings. Here we consider LD in the context of Participatory Budgeting (PB), which is a direct democracy approach to budgeting, most usually done in municipal budgeting processes. In particular, we study Knapsack Voting, in which PB voters approve projects, such that the sum of costs of projects each voter approves must respect the budget limit. We observe possible inconsistencies, as the cost of voter-approved projects may go over the budget limit after resolving delegations. We offer ways to overcome them by studying the computational complexity of updating as few delegations as possible to arrive  after following all project delegations  to a consistent profile.

AAMAS 2021

Preserving Consistency for Liquid Knapsack Voting

AAMAS is the largest and most influential conference in the area of agents and multiagent systems, bringing together researchers and practitioners in all areas of agent technology and providing and internationally renowned high-profile forum for publishing and finding out about the latest developments in the field. AAMAS is the flagship conference of the non-profit International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).  

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poster

We tackle the problem of allocating teams to tasks. For that, we propose a novel allocation problem that matches teams with tasks based on the similarity between the competencies required by the tasks and the competencies offered by teams. We formally cast our problem as an optimisation problem, characterise the size of its search space and outline a heuristic approach to solve it.

Towards a Competence-Based Approach to Allocate Teams to Tasks

In this paper, we extend the unavailable candidate model (Tyler Lu and Craig Boutilier, The Unavailable Candidate Model : a Decision-Theoretic View of Social Choice, 2010) and present two new voting rules based on a finer notion of disagreement, called dissatisfaction, which depends on the ranks of the candidates, considered among all the candidates (
 rule) or only among the available candidates (
 rule). We provide algorithmic results for the two rules and show that apparently very different voting rules such as scoring rules or Kemeny rule can be unified under the same aggregation concept: expectation of dissatisfaction under the availability distribution.

Rank Aggregation by Dissatisfaction Minimisation in the Unavailable Candidate Model

A finite-time consensus protocol is developed for a connected network of agents, where communication between agents occurs locally, some of the agents are malicious, and the non-malicious or cooperative agents do not know the identities of the malicious ones. The agents are modeled with first-order dynamics, and the inputs to each agent that enable consensus are designed using the principles of sliding mode control (SMC). The use of the SMC algorithm guarantees finite-time consensus and ensures that in the transient stage, the agents' states are contained within the convex hull formed by their initial conditions (ICs). With this feature and by modeling the network as a connected graph, the protocol guarantees consensus amongst the cooperative agents when the malicious agents transmit values of their states lying outside the convex hull of ICs, and the graph formed by the cooperative agents with the removal of the malicious agents is strongly connected. The protocol does not require a cooperative agent to know the number of malicious or other cooperative agents in the network, and is based only on local communication.

Finite-time Consensus in the Presence of Malicious Agents

We explore the possibility of an alternative cryptocurrency that is egalitarian in control, just in the distribution of its created wealth, and forms and grows in a grassroots way; we analyze it via a mathematical entity called a 
 Our main result states sufficient conditions for the establishment of 1:1 exchange rates and distributive justice in a currency network.

Egalitarian and Just Digital Currency Networks

Crowdfunding has become an effective way of raising capital for
developing and producing new products. In a typical crowdfunding campaign, a fundraiser (a seller) sets a product pre-buy price
and a campaign success threshold. Consumers can indicate their
willingness to pay the pre-buy price now, in exchange of a product
in the future. Only when the number of consumers who commit to
pre-buy exceeds the threshold, the crowdfunding is successful and
the seller gets the corresponding pre-buy payments.
A series of works has modeled crowdfunding as imperfect information games, where each player (potential contributor) has a
private valuation for the product, and has characterized the equilibrium behavior for some specific settings [1–4]. Other works focus
on the effectiveness or the moral hazard of the crowdfunding campaigns by regarding it as an option to raise money for either private
[5, 9, 10] or public projects [6–8].
However, the strategic aspect of crowdfunding from the seller’s
perspective hasn’t attracted its deserved attention. In this paper,
we take a mechanism design perspective and explore how a seller
can design crowdfunding campaigns to maximize his profit. In
addition to choosing the pre-buy price and the campaign success
threshold for a crowdfunding campaign, the seller in our paper can
consider two richer design variants: (1) choose two price-threshold
pairs where a pre-buy price discount is given when the number
of committed buyers exceeds the larger threshold, and (2) offer
two differentiating products (simplified vs. standard) and set two
success thresholds such that the advanced product will be delivered
if the larger threshold is reached. We examine the optimal profit
achieved in each scheme. Somewhat surprisingly, the richer design
variants may not improve the seller’s profit.

Optimal Crowdfunding Design

In swarm robotics, research mainly follows a theoretical approach that considers robot systems in the abstract, where the complexity and capabilities of the underlying model are often reduced to their minimum. One general and well-investigated model is &#248;blot, where the robots are silent, anonymous, and oblivious. In this work, we introduce MOBLOT, a model that extends &#248;blot to address a larger spectrum of cases. MOBLOT stands for molecular oblivious robots: like atoms combine themselves to form molecules, in MOBLOT simple robots can move to form more complex computational units, having an extent and different capabilities with respect to robots; like molecules combine themselves to form the matter, in MOBLOT the complex structures can exploit their own capabilities to arrange themselves to form any shape defining an acceptable final structure.   In MOBLOT, we formally define the Matter Formation (MF) problem and, as a preliminary general result, we provide a necessary condition for its solvability which relies on symmetricity.  Informally, the symmetricity of a configuration measures the amount of symmetries of the robots' disposal.  We actually show how dealing with molecules can resolve in some cases the symmetry breaking issue where &#248;blot cannot. Finally, we provide a case study for MOBLOT, that is, a representative MF problem along with a resolution distributed algorithm.

MOBLOT: Molecular Oblivious Robots

Multi-agent influence diagrams (MAIDs) are a popular form of graphical model that, for certain classes of games, have been shown to offer key complexity and explainability advantages over traditional extensive form game (EFG) representations. In this paper, we extend previous work on MAIDs by introducing the concept of a MAID subgame, as well as subgame perfect and trembling hand perfect equilibrium refinements. We then prove several equivalence results between MAIDs and EFGs. Finally, we describe an open source implementation for reasoning about MAIDs and computing their equilibria.

Equilibrium Refinements for Multi-Agent Influence Diagrams: Theory and Practice

This paper presents new algorithms and theoretical results for solutions to Multi-action Multi-armed Restless Bandits, an important but insufficiently studied generalization of traditional Multi-armed Restless Bandits (MARBs). Though MARBs are popular for modeling many problems, they are restricted to binary actions, i.e., "to act or not to act". This renders them unable to capture critical complexities faced by planners in real domains, such as a system manager balancing maintenance, repair, and job scheduling, or a health worker deciding among treatments for a given patient. Limited previous work on Multi-action MARBs has only been specialized to sub-problems. Here we derive multiple algorithms for use on general Multi-action MARBs using Lagrangian relaxation techniques, leading to the following contributions: (i) We develop BLam, a bound optimization algorithm which leverages problem convexity to quickly and provably converge to the well-performing Lagrange policy; (ii) We develop SampleLam, a fast sampling technique for estimating the Lagrange policy, and derive a concentration bound to investigate its convergence properties; (iii) We derive best and worst case computational complexities for our algorithms as well as our main competitor; (iv) We provide experimental results comparing our algorithms to baselines on simulated distributions, including one motivated by a real-world community health intervention task. Our approach achieves significant, up to ten-fold speedups over more general methods without sacrificing performance and is widely applicable across general Multi-action MARBs. Code is available at https://github.com/killian-34/MAMARB-Lagrange-Policies.

Beyond "To Act or Not to Act": Fast Lagrangian Approaches to General Multi-Action Restless Bandits

Multi-agent reinforcement learning (MARL) requires coordination to efficiently solve certain tasks. Fully centralized control is often infeasible in such domains due to the size of joint action spaces. Coordination graph based formalization allows reasoning about the joint action based on the structure of interactions. However,they often require domain expertise in their design. This paper introduces the deep implicit coordination graph (DICG) architecture for such scenarios. DICG consists of a module for inferring the dynamic coordination graph structure which is then used by a graph neural network based module to learn to implicitly reason about the joint actions or values. DICG allows learning the tradeoff between full centralization and decentralization via standard actor-critic methods to significantly improve coordination for domains with large number of agents. We apply DICG to both centralized-training-centralized-execution and centralized-training-decentralized-execution regimes. We demonstrate that DICG solves the relative over generalization pathology in predatory-prey tasks as well as outperforms various MARL baselines on the challenging StarCraft II Multi-agent Challenge (SMAC) and traffic junction environments.

Deep Implicit Coordination Graphs for Multi-agent Reinforcement Learning

Partially Observable Monte-Carlo Planning (POMCP) is a powerful online algorithm able to generate approximate policies for large Partially Observable Markov Decision Processes. The online nature of this method supports scalability by avoiding complete policy representation. The lack of an explicit representation however hinders interpretability. In this work, we propose a methodology based on Satisfiability Modulo Theory (SMT) for analyzing POMCP policies by inspecting their traces, namely sequences of belief-action-observation triplets generated by the algorithm. The proposed method explores local properties of policy behavior to identify unexpected decisions. We propose an iterative process of trace analysis consisting of three main steps, i) the definition of a 
 by means of a parametric logical formula describing (probabilistic) relationships between beliefs and actions, ii) the generation of an 
 by computing the parameters of the logical formula that maximize the number of satisfied clauses (solving a MAX-SMT problem), iii) the analysis of the generated logical formula and the related decision boundaries for identifying unexpected decisions made by POMCP with respect to the original question. We evaluate our approach on Tiger, a standard benchmark for POMDPs, and a real-world problem related to mobile robot navigation. Results show that the approach can exploit human knowledge on the domain, outperforming state-of-the-art anomaly detection methods in identifying unexpected decisions. An improvement of the Area Under Curve up to 47% has been achieved in our tests.

Preserving Consistency for Liquid Knapsack Voting

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