As robots' manipulation capabilities improve for pick-and-place tasks (e.g., object packing, sorting, and kitting), methods focused on understanding human-acceptable object configurations remain limited expressively with regard to capturing spatial relationships important to humans. To advance robotic understanding of human rules for object arrangement, we introduce positionally-augmented RCC (PARCC), a formal logic framework based on region connection calculus (RCC) for describing the relative position of objects in space. Additionally, we introduce an inference algorithm for learning PARCC specifications via demonstrations. Finally, we present the results from a human study, which demonstrate our framework's ability to capture a human's intended specification and the benefits of learning from demonstration approaches over human-provided specifications.
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Credit Assignment and Fine-Tuning Enhanced Reinforcement Learning for Collaborative Spatial Crowdsourcing
PDF ↗Collaborative spatial crowdsourcing leverages distributed workers' collective intelligence to accomplish spatial tasks. A central challenge is to efficiently assign suitable workers to collaborate on these tasks. Although mainstream reinforcement learning (RL) methods have proven effective in task allocation, they face two key obstacles: delayed reward feedback and non-stationary data distributions, both hindering optimal allocation and collaborative efficiency. To address these limitations, we propose CAFE (credit assignment and fine-tuning enhanced), a novel multi-agent RL framework for spatial crowdsourcing. CAFE introduces a credit assignment mechanism that distributes rewards based on workers' contributions and spatiotemporal constraints, coupled with bi-level meta-optimization to jointly optimize credit assignment and RL policy. To handle non-stationary spatial task distributions, CAFE employs an adaptive fine-tuning procedure that efficiently adjusts credit assignment parameters while preserving collaborative knowledge. Experiments on two real-world datasets validate the effectiveness of our framework, demonstrating superior performance in terms of task completion and equitable reward redistribution.
Transformer-based Spiking Neural Networks (SNNs) introduce a novel event-driven self-attention paradigm that combines the high performance of Transformers with the energy efficiency of SNNs. However, the larger model size and increased computational demands of the Transformer structure limit their practicality in resource-constrained scenarios. In this paper, we integrate binarization techniques into Transformer-based SNNs and propose the Binary Event-Driven Spiking Transformer, i.e. BESTformer. The proposed BESTformer can significantly reduce storage and computational demands by representing weights and attention maps with a mere 1-bit. However, BESTformer suffers from a severe performance drop from its full-precision counterpart due to the limited representation capability of binarization. To address this issue, we propose a Coupled Information Enhancement (CIE) method, which consists of a reversible framework and information enhancement distillation. By maximizing the mutual information between the binary model and its full-precision counterpart, the CIE method effectively mitigates the performance degradation of the BESTformer. Extensive experiments on static and neuromorphic datasets demonstrate that our method achieves superior performance to other binary SNNs, showcasing its potential as a compact yet high-performance model for resource-limited edge devices. The repository of this paper is available at https://github.com/CaoHLin/BESTFormer.
In collaborative tasks, autonomous agents fall short of humans in their capability to quickly adapt to new and unfamiliar teammates. We posit that a limiting factor for zero-shot coordination is the lack of shared task abstractions, a mechanism humans rely on to implicitly align with teammates. To address this gap, we introduce HA^2: Hierarchical Ad Hoc Agents, a framework leveraging hierarchical reinforcement learning to mimic the structured approach humans use in collaboration. We evaluate HA^2 in the Overcooked environment, demonstrating statistically significant improvement over existing baselines when paired with both unseen agents and humans, providing better resilience to environmental shifts, and outperforming all state-of-the-art methods.
Consider a market with a seller and many buyers. The seller has a kind of item for sale to the buyers. The items have a quality and each buyer has a private type. The quality is only known to the seller, and the buyers only have a prior belief of the quality. A third party (e.g., intermediaries or product reviewers) is able to reveal information about the actual quality by using a so-called signaling scheme. After receiving the information, buyers can update their beliefs accordingly and decide whether to buy the items. We consider the third party's problem of maximizing the purchasing probability by sending signals. However, the optimal signaling scheme has implementation issues, as the number of signals in the optimal scheme is the same as the number of buyer types, which can be exceedingly large or even infinite. We therefore investigate whether a finite and limited set of signals could still approximate the performance of the optimal signaling scheme. Unfortunately, our results show that with a finite number of signals, no signaling scheme can achieve a certain fraction of the performance of the optimal signaling scheme. This limitation persists even with the regularity or the monotone hazard rate assumption. Nevertheless, we identify a mild technical condition under which the third party can approximate the optimal performance within a constant factor by employing only two signals. We also conduct extensive experiments to substantiate our theoretic results. These experiments compare the performance of using a small signal set across different value distributions. Despite the negative results, our experiment results show that using only a small number of signals is able to achieve a fairly reasonable performance in average cases.
In this paper, we revisit the problem of fair allocation with subsidy. We first consider the allocation of m indivisible chores to n agents with additive (dis)utility functions. Under the assumption that the maximum (dis)utility of an item can be compensated by one dollar, Wu et al. (WINE 2023) showed that a total of n/4 dollars suffices to guarantee a proportional allocation by rounding fractional allocations. Their subsidy guarantee is optimal when n is even. For odd n, there is still a small gap between the upper and lower bounds for the total subsidy. In this paper, we propose a much simpler algorithm for the problem, which does not require rounding fractional allocations, and achieves an optimal subsidy guarantee for all values of n. Different from existing works, our algorithm does not require the computation and rounding of fractional allocations and admits a much simpler analysis. We further show that our algorithm and analysis framework can be extended to the mixture of (subjective) goods and chores, achieving the optimal subsidy guarantee.
We consider the problem of fair allocation of m indivisible items to a group of n agents with subsidies (money). We address scenarios where agents have general additive cost/utility functions. Our work primarily focuses on the special case of three agents. Assuming that the maximum cost/utility of an item to an agent can be compensated by one dollar, we demonstrate that a total subsidy of 1/6 dollars is sufficient to ensure the existence of Maximin Share (MMS) allocations for both goods and chores. Additionally, we provide examples to establish the lower bounds of the required subsidies.
We study a practical centralized matching problem which assigns children to daycare centers. The collective preferences of siblings from the same family introduce complementarities, which can lead to the absence of stable matchings, as observed in the hospital-doctor matching problems involving couples. Intriguingly, stable matchings are consistently observed in real-world daycare markets, despite the prevalence of sibling applicants. We conduct a probabilistic analysis of large random markets to examine the existence of stable matchings in such markets. Specifically, we focus on scenarios where daycare centers have similar priorities over children, a common characteristic in real-world markets. Our analysis reveals that as the market size approaches infinity, the likelihood of stable matchings existing converges to 1. To facilitate our exploration, we refine an existing heuristic algorithm to address a more rigorous stability concept, as the original one may fail to meet this criterion. Through extensive experiments on both real-world and synthetic datasets, we demonstrate the effectiveness of our revised algorithm in identifying stable matchings, particularly when daycare priorities exhibit high similarity.
We study fair division of indivisible goods under the maximin share (MMS) fairness criterion in settings where agents are grouped into a small number of types, with agents within each type having identical valuations. For the special case of a single type, an exact MMS allocation is always guaranteed to exist. However, for two or more distinct agent types, exact MMS allocations do not always exist, shifting the focus to establishing the existence of approximate-MMS allocations. A series of works over the last decade has resulted in the best-known approximation guarantee of 3/4 + 3/3836. In this paper, we improve the approximation guarantees for settings where agents are grouped into two or three types, a scenario that arises in many practical settings. Specifically, we present novel algorithms that guarantee a 4/5-MMS allocation for two agent types and a 16/21-MMS allocation for three agent types. Our approach leverages the MMS partition of the majority type and adapts it to provide improved fairness guarantees for all types.
We consider a spatial voting model where both candidates and voters are positioned in the d-dimensional Euclidean space, and each voter ranks candidates based on their proximity to the voter's ideal point. We focus on the scenario where the given information about the locations of the voters' ideal points is incomplete; for each dimension, only an interval of possible values is known. In this context, we investigate the computational complexity of determining the possible winners under positional scoring rules. Our results show that the possible winner problem in one dimension is solvable in polynomial time for all k-truncated voting rules with constant k. Moreover, for some scoring rules for which the possible winner problem is NP-complete, such as approval voting for any dimension or k-approval for two or more dimensions, we give an FPT algorithm parameterized by the number of candidates. Finally, we classify tractable and intractable settings of the em weighted possible winner problem in one dimension, and resolve the computational complexity of the weighted case for all two-valued positional scoring rules when d=1.
We study a budget aggregation setting where voters express their preferred allocation of a fixed budget over a set of alternatives, and a mechanism aggregates these preferences into a single output allocation. Motivated by scenarios in which the budget is not perfectly divisible, we depart from the prevailing literature by restricting the mechanism to output allocations that assign integral amounts. This seemingly minor deviation has significant implications for the existence of truthful mechanisms. Specifically, when voters can propose fractional allocations, we demonstrate that the Gibbard-Satterthwaite theorem can be extended to our setting. In contrast, when voters are restricted to integral ballots, we identify a class of truthful mechanisms by adapting moving-phantom mechanisms to our context. Finally, we show that while a weak form of proportionality can be achieved alongside truthfulness, stronger proportionality notions derived from approval-based committee voting are incompatible with truthfulness.
We study the problem of design of strategy-proof in expectation (SP) mechanisms for facility location on a cycle, with the objective of minimizing the sum of costs of n agents. We show that there exists an SP mechanism that attains an approximation ratio of 7/4 with respect to the sum of costs of the agents, thus improving the best known upper bound of 2 - 2/n in the cases of n ≥ 5. The mechanism obtaining the bound randomizes between two mechanisms known in the literature: the Random Dictator (RD) and the Proportional Circle Distance (PCD) mechanism of Meir (2019). To prove the result, we propose a cycle-cutting technique that allows for estimating the problem on a cycle by a problem on a line.
We consider the Hospitals/Residents (HR) problem in the presence of ties in preference lists of hospitals. Among the three notions of stability, viz. weak, strong, and super stability, we focus on strong stability. Strong stability is appealing both theoretically and practically; however, its existence is not guaranteed. In this paper, our objective is to optimally augment the quotas of hospitals to ensure that a strongly stable matching exists in the modified instance. Such an augmentation is guaranteed to exist when resident preference lists are strict. We explore two natural optimization criteria: (i) minimizing the total capacity increase across all hospitals (MINSUM) and (ii) minimizing the maximum capacity increase for any hospital (MINMAX). We show that the MINSUM problem admits a polynomial-time algorithm, whereas the MINMAX problem is NP-hard. We prove an analogue of the Rural Hospitals theorem for the MINSUM problem. When each hospital incurs a cost for a unit increase in its quota, the MINSUM problem becomes NP-hard, even for 0/1 costs. In fact, we show that the problem cannot be approximated to any multiplicative factor. We also present a polynomial-time algorithm for optimal MINSUM augmentation when a specified subset of edges is required to be included in the matching.
In an approval-based committee election, the goal is to select a committee consisting of k out of m candidates, based on n voters who each approve an arbitrary number of the candidates. The core of such an election consists of all committees that satisfy a certain stability property which implies proportional representation. In particular, committees in the core cannot be "objected to" by a coalition of voters who is underrepresented. The notion of the core was proposed in 2016, but it has remained an open problem whether it is always non-empty. We prove that core committees always exist when k ≤ 8, for any number of candidates m and any number of voters n, by showing that the Proportional Approval Voting (PAV) rule, proposed by Thiele in 1895, always satisfies the core when k ≤ 7 and always selects at least one committee in the core when k = 8. We also develop an artificial rule based on recursive application of PAV, and use it to show that the core is non-empty whenever there are m ≤ 15 candidates, for any committee size k ≤ m and any number of voters n. These results are obtained with the help of computer search using linear programs.
We consider a class of jump games in which agents of different types occupy the nodes of a graph aiming to maximize the variety of types in their neighborhood. In particular, each agent derives a utility equal to the number of types different from its own in its neighborhood. We show that the jump game induced by the strategic behavior of the agents (who aim to maximize their utility) may in general have improving response cycles, but is a potential game under any of the following four conditions: there are only two types of agents; or exactly one empty node; or the graph is of degree at most 2; or the graph is 3-regular and there are two empty nodes. Additionally, we show that on trees, cylinder graphs, and tori, there is always an equilibrium. Finally, we show tight bounds on the price of anarchy with respect to two different measures of diversity: the social welfare (the total utility of the agents) and the number of colorful edges (that connect agents of different types).
We study the problem of computing an approximate Nash equilibrium of a game whose strategy space is continuous without access to gradients of the utility function. Lack of access to gradients is common in reinforcement learning settings, where the environment is treated as a black box, as well as equilibrium finding in mechanisms such as auctions, where the mechanism's payoffs are discontinuous in the players' actions. To tackle this problem, we turn to zeroth-order optimization techniques that combine pseudo-gradients with equilibrium-finding dynamics. Specifically, we introduce a new technique that requires a number of utility function evaluations per iteration that is constant rather than linear in the number of players. It achieves this by performing a single joint perturbation on all players' strategies, rather than perturbing each one individually. This is very important for many-player games, especially when the utility function is expensive to compute in terms of wall time, memory, money, or other resources. We evaluate our approach on various games, including auctions, which have important real-world applications. Our approach yields a dramatic improvement in performance in terms of the wall time required to reach an approximate Nash equilibrium.
When dividing items among agents, two of the most widely studied fairness notions are envy-freeness and proportionality. We consider a setting where m chores are allocated to n agents and the disutility of each chore for each agent is drawn from a probability distribution. We show that an envy-free allocation exists with high probability provided that m >= 2n, and moreover, m must be at least n+Theta(n) in order for the existence to hold. On the other hand, we prove that a proportional allocation is likely to exist as long as m = omega(1), and this threshold is asymptotically tight. Our results reveal a clear contrast with the allocation of goods, where a larger number of items is necessary to ensure existence for both notions.
Several resource allocation settings involve agents with unequal entitlements represented by weights. We analyze weighted fair division from an asymptotic perspective: if m items are divided among n agents whose utilities are independently sampled from a probability distribution, when is it likely that a fair allocation exist? We show that if the ratio between the weights is bounded, a weighted envy-free allocation exists with high probability provided that m = Omega(n log n / log log n), generalizing a prior unweighted result. For weighted proportionality, we establish a sharp threshold of m = n / (1 - \mu) for the transition from non-existence to existence, where \mu in (0,1) denotes the mean of the distribution. In addition, we prove that for two agents, a weighted envy-free (and weighted proportional) allocation is likely to exist if m = omega(sqrt{r}), where r denotes the ratio between the two weights.
Consider a social network where each node (user) is blue or red, corresponding to positive or negative opinion on a topic. In the voter model, in discrete time rounds, each node picks a neighbour uniformly at random and adopts its colour. Despite its significant popularity, this model does not capture some fundamental real-world characteristics such as the difference in the strengths of connections, individuals with no initial opinion, and users who are reluctant to update. To address these issues, we introduce a generalisation of the voter model. We study the problem of selecting a set of seed blue nodes to maximise the expected number of blue nodes after some rounds. We prove that the problem is NP-hard and provide a polynomial time approximation algorithm with the best possible approximation guarantee. Our experiments on real-world and synthetic graph data demonstrate that the proposed algorithm outperforms other algorithms. We also prove that the process could take an exponential number of rounds to converge. However, if we limit ourselves to strongly connected graphs, the convergence time is polynomial and the convergence period (size of the stationary configuration) is bounded by the highest common divisor of cycle lengths in the network.
Resource competition problems are often modeled using Colonel Blotto games, where players take simultaneous actions. However, many real-world scenarios involve sequential decision-making rather than simultaneous moves. To model these dynamics, we represent the Lottery Colonel Blotto game as a Stackelberg game, in which one player, the leader, commits to a strategy first, and the other player, the follower, responds. We derive the Stackelberg equilibrium for this game, formulating the leader's strategy as a bi-level optimization problem. To solve this, we develop a constructive method based on iterative game reductions, which allows us to efficiently compute the leader’s optimal commitment strategy in polynomial time. Additionally, we identify the conditions under which the Stackelberg equilibrium coincides with the Nash equilibrium. Specifically, this occurs when the budget ratio between the leader and the follower equals a certain threshold, which we can calculate in closed form. In some instances, we observe that when the leader’s budget exceeds this threshold, both players achieve higher utilities in the Stackelberg equilibrium compared to the Nash equilibrium. Lastly, we show that, in the best case, the leader can achieve an infinite utility improvement by making an optimal first move compared to the Nash equilibrium.