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Various voting rules are based on ranking the candidates by scores induced by aggregating voter preferences. A winner (respectively, unique winner) is a candidate who receives a score not smaller than (respectively, strictly greater than) the remaining candidates. Examples of such rules include the positional scoring rules and the Bucklin, Copeland, and Maximin rules. When voter preferences are known in an incomplete manner as partial orders, a candidate can be a possible/necessary winner based on the possibilities of completing the partial votes. Past research has studied in depth the computational problems of determining the possible and necessary winners and unique winners. These problems are all special cases of reasoning about the range of possible positions of a candidate under different tiebreakers. We investigate the complexity of determining this range, and particularly the extremal positions. Among our results, we establish that finding each of the minimal and maximal positions is NP-hard for each of the above rules, including all positional scoring rules, pure or not. Hence, none of the tractable variants of necessary/possible winner determination remain tractable for extremal position determination. Tractability can be retained when reasoning about the top- k  positions for a fixed  k . Yet, exceptional is Maximin where it is tractable to decide whether the maximal rank is  k  for $k=1$ (necessary winning) but it becomes intractable for all $k&gt;1$.

AAMAS 2021

Computing the Extremal Possible Ranks with Incomplete Preferences

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Various voting rules are based on ranking the candidates by scores induced by aggregating voter preferences. A winner (respectively, unique winner) is a candidate who receives a score not smaller than (respectively, strictly greater than) the remaining candidates. Examples of such rules include the positional scoring rules and the Bucklin, Copeland, and Maximin rules. When voter preferences are known in an incomplete manner as partial orders, a candidate can be a possible/necessary winner based on the possibilities of completing the partial votes. Past research has studied in depth the computational problems of determining the possible and necessary winners and unique winners. These problems are all special cases of reasoning about the range of possible positions of a candidate under different tiebreakers. We investigate the complexity of determining this range, and particularly the extremal positions. Among our results, we establish that finding each of the minimal and maximal positions is NP-hard for each of the above rules, including all positional scoring rules, pure or not. Hence, none of the tractable variants of necessary/possible winner determination remain tractable for extremal position determination. Tractability can be retained when reasoning about the top- k  positions for a fixed  k . Yet, exceptional is Maximin where it is tractable to decide whether the maximal rank is  k  for $k=1$ (necessary winning) but it becomes intractable for all $k>1$.

technical paper

We present a methodology to robustly estimate the competitive equilibria (CE) of combinatorial markets under the assumption that buyers do not know their precise valuations for bundles of goods, but instead can only provide noisy estimates. We first show tight lower- and upper-bounds on the buyers' utility loss, and hence the set of CE, given a uniform approximation of one market by another. We then present two probably-approximately-correct algorithms for learning CE with finite-sample guarantees. The first is a baseline and the second leverages a connection between the first welfare theorem of economics and uniform approximations to adaptively prune value queries when it is determined that they are provably not part of a CE. Extensive experimentation shows that pruning achieves better estimates than the baseline with far fewer samples.

Learning Competitive Equilibria in Noisy Combinatorial Markets

A key problem in network analysis is the influence maximization problem, which consists of finding a set S of at most k seed users in a social network, such that the spread of information from S is maximized. We investigate the problem of choosing the best set of seeds when there exists an unknown pre-existing set of seed nodes. Our work extends the one of Chen and Teng (WWW'17) who introduced the so-called Shapley centrality of a node to measure the efficiency of nodes acting as seeds within a pre-existing but unknown set of seeds. We instead consider the question: Which set of cardinality k to target in this kind of scenario? The resulting optimization problem reveals very challenging, that is, assuming common computational complexity conjectures, we obtain strong hardness of approximation results. Nevertheless, we design a greedy algorithm which achieves an approximation factor of 1-1/e k  -ε for any ε > 0, showing that not all is lost in settings where k is bounded.

Maximizing Influence-Based Group Shapley Centrality

We present a model for the strategic selection of party nominees, where competing groups choose their representatives based on the expected electoral returns. Technically, we look at a generalisation of the Hotelling-Downs model, where each nominee has a predefined position on the political spectrum and attracts the closest voters compared to all other representatives. Within this framework we explore the algorithmic properties of Nash equilibria, which are not guaranteed to exist even in two party competitions. We show that finding a Nash equilibrium is NP-complete for the general case. However, if there are only two competing parties, this can be achieved in linear time. The results readily extend to games with restricted positioning options for the players involved, such as facility location and Voronoi games.

A Hotelling-Downs Framework for Party Nominees

The study of exploration in the domain of decision making has a long history but remains actively debated. From the vast literature that addressed this topic for decades under various points of view (e.g., developmental psychology, experimental design, artificial intelligence), intrinsic motivation emerged as a concept that can practically be transferred to artificial agents. Especially, in the recent field of Deep Reinforcement Learning (RL), agents implement such a concept (mainly using a novelty argument) in the shape of an exploration bonus, added to the task reward, that encourages visiting the whole environment. This approach is supported by the large amount of theory on RL for which convergence to optimality assumes exhaustive exploration. Yet, Human Beings and mammals do not exhaustively explore the world and their motivation is not only based on novelty but also on various other factors (e.g., curiosity, fun, style, pleasure, safety, competition, etc.). They optimize for life-long learning and train to learn transferable skills in playgrounds without obvious goals. They also apply innate or learned priors to save time and stay safe. For these reasons, we propose to learn an exploration bonus from demonstrations that could transfer these motivations to an artificial agent with little assumptions about their rationale. Using an inverse RL approach, we show that complex exploration behaviors, reflecting different motivations, can be learnt and efficiently used by RL agents to solve tasks for which exhaustive exploration is prohibitive.

Show Me the Way: Intrinsic Motivation from Demonstrations

We investigate the problem of computing the probability of winning in an election where voter attendance is uncertain. More precisely, we study the setting where, in addition to a total ordering of the candidates, each voter is associated with a probability of attending the poll, and the attendances of different voters are probabilistically independent. We show that the probability of winning can be computed in polynomial time for the plurality and veto rules. However, it is computationally hard (#P-hard) for various other rules, including k-approval and k-veto for $k>1$, Borda, Condorcet, and Maximin. For some of these rules, it is even hard to find a multiplicative approximation since it is already hard to determine whether this probability is nonzero. In contrast, we devise a fully polynomial-time randomized approximation scheme (FPRAS) for the complement probability, namely the probability of losing, for every positional scoring rule (with polynomial scores), as well as for the Condorcet rule.

Probabilistic Inference of Winners in Elections by Independent Random Voters

Cross-Entropy Method (CEM) is a gradient-free direct policy search method, which has greater stability and is insensitive to hyper-parameter tuning. CEM bears similarity to population-based evolutionary methods, but, rather than using a population it uses a distribution over candidate solutions (policies in our case). Usually, a natural exponential family distribution such as multivariate Gaussian is used to parameterize the policy distribution. Using a multivariate Gaussian limits the quality of CEM policies as the search becomes confined to a less representative subspace. We address this drawback by using an adversarially-trained hypernetwork, enabling a richer and complex representation of the policy distribution. To achieve better training stability and faster convergence, we use a multivariate Gaussian CEM policy to guide our adversarial training process. Experiments demonstrate that our approach outperforms state-of-the-art CEM-based methods by $15.8%$ in terms of rewards while achieving faster convergence. Results also show that our approach is less sensitive to hyper-parameters than other deep-RL methods such as REINFORCE, DDPG and DQN.

Learning Complex Policy Distribution with CEM Guided Adversarial Hypernetwork

We consider exploration tasks in which an autonomous mobile robot incrementally builds maps of initially unknown indoor environments. In such tasks, the robot makes a sequence of decisions on where to move next that, usually, are based on knowledge about the observed parts of the environment.   In this paper, we present an approach that exploits a prediction of the geometric structure of the unknown parts of an environment to improve exploration performance. In particular, we leverage an existing method that reconstructs the layout of an environment starting from a partial grid map and that predicts the shape of partially observed rooms on the basis of geometric features representing the regularities of the indoor environment. Then, we originally employ the predicted layout to estimate the amount of new area the robot would observe from candidate locations in order to inform the selection of the next best location and to early stop the exploration when no further relevant area is expected to be discovered. Experimental activities show that our approach is able to exploit the predicted layout of partially observed rooms in order to speed up the exploration.

Exploration of Indoor Environments through Predicting the Layout of Partially Observed Rooms

The real world is awash with multi-agent problems that require collective action by self-interested agents, from the routing of packets across a computer network to the management of irrigation systems. Such systems have local incentives for individuals, whose behavior has an impact on the global outcome for the group. Given appropriate mechanisms describing agent interaction, groups may achieve socially beneficial outcomes, even in the face of short-term selfish incentives. In many cases, collective action problems possess an underlying graph structure, whose topology crucially determines the relationship between local decisions and emergent global effects. Such scenarios have received great attention through the lens of network games. However, this abstraction typically collapses important dimensions, such as geometry and time, relevant to the design of mechanisms promoting cooperation. In parallel work, multi-agent deep reinforcement learning has shown great promise in modelling the emergence of self-organized cooperation in complex gridworld domains. Here we apply this paradigm in graph-structured collective action problems.

Modelling Cooperation in Network Games with Spatio-Temporal Complexity

We present an ascending-price mechanism for a multi-sided market with a variety of participants, such as manufacturers, logistics agents, insurance providers, and assemblers. Each deal in the market may consist of a combination of agents from separate categories, and different such combinations are simultaneously allowed. This flexibility lets multiple intersecting markets be resolved as a single global market. Our mechanism is obviously-truthful, strongly budget-balanced, individually rational, and attains almost the optimal gain-from-trade when the market is sufficiently large.

A Global Multi-Sided Market with Ascending-Price Mechanism

Trading mechanisms play a fundamental role in the health of financial markets. For example, it is believed that continuous double auctions constitute fertile soil for predatory behaviour and toxic order flows. To this end, frequent call markets have been proposed as an alternative design choice to address the latency arbitrage opportunities built in those markets. This paper studies the extent to which adaptive rules to define the length of the clearing intervals affect the performance of frequent call markets.

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Learning Competitive Equilibria in Noisy Combinatorial Markets

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Next from AAMAS 2021

Learning Competitive Equilibria in Noisy Combinatorial Markets

Similar lecture

Classifying the Complexity of the Possible Winner Problem on Partial Chains

Stay up to date with the latest Underline news!

PRESENTATIONS

CONFERENCES

COMPANY

RESOURCES

Downloads