Chance-Constrained Active Inference

Active inference (ActInf) is an emerging theory that explains perception and action in biological agents in terms of minimizing a free energy bound on Bayesian surprise. Goal-directed behavior is elicited by introducing prior beliefs on the underlying generative model. In contrast to prior beliefs, which constrain all realizations of a random variable, we propose an alternative approach through chance constraints, which allow for a (typically small) probability of constraint violation, and demonstrate how such constraints can be used as intrinsic drivers for goal-directed behavior in ActInf. We illustrate how chance-constrained ActInf weights all imposed (prior) constraints on the generative model, allowing, for example, for a trade-off between robust control and empirical chance constraint violation. Second, we interpret the proposed solution within a message passing framework. Interestingly, the message passing interpretation is not only relevant to the context of ActInf, but also provides a general-purpose approach that can account for chance constraints on graphical models. The chance constraint message updates can then be readily combined with other prederived message update rules without the need for custom derivations. The proposed chance-constrained message passing framework thus accelerates the search for workable models in general and can be used to complement message-passing formulations on generative neural models.

Spanish embedded question island effects revisited: an experimental study

It is often reported that embedded questions (EQs) are not syntactic islands in Spanish. However, some authors have observed that the acceptability of filler-gap dependencies (FGDs) into Spanish EQs varies with the EQ-embedding verb: FGDs into EQs under responsive verbs (e.g., know) do not result in island effects, but FGDs into EQs under rogative verbs (e.g., ask) do yield island effects. One account attributes the contrast to a structural difference between the two EQs, due to which ask-EQs violate Bounding constraints, but know-EQs do not. In two acceptability studies we investigated the reliability of verb-dependent island effects in EQs introduced by si ‘whether’ and cuándo ‘when’. We found no qualitative acceptability differences between ask and know EQ-island sentences, suggesting that the syntactic islandhood of Spanish EQs is not verb-dependent. Nevertheless, average island effects were numerically greater with ask, suggesting the presence of a non-syntactic constraint. In addition, FGDs into whether-EQs were generally acceptable, whereas FGDs into when-EQs obtained unacceptable average ratings and highly variable judgments. We argue that in neither case there is a Bounding constraint violation. Instead we explore alternative potential explanations for the differences in terms of features, presuppositions and processing pressures.

Stability in Matching Markets with Complex Constraints

We develop a model of many-to-one matching markets in which agents with multiunit demand aim to maximize a cardinal linear objective subject to multidimensional knapsack constraints. The choice functions of agents with multiunit demand are therefore not substitutable. As a result, pairwise stable matchings may not exist and even when they do, may be highly inefficient. We provide an algorithm that finds a group-stable matching that approximately satisfies all the multidimensional knapsack constraints. The novel ingredient in our algorithm is a combination of matching with contracts and Scarf’s Lemma. We show that the degree of the constraint violation under our algorithm is proportional to the sparsity of the constraint matrix. The algorithm, therefore, provides practical constraint violation bounds for applications in contexts, such as refugee resettlement, day care allocation, and college admissions with diversity requirements. Simulations using refugee resettlement data show that our approach produces outcomes that are not only more stable, but also more efficient than the outcomes of the Deferred Acceptance algorithm. Moreover, simulations suggest that in practice, constraint violations under our algorithm would be even smaller than the theoretical bounds. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.