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Information Socialtaxis and Efficient Collective Behavior Emerging In Information socialtaxis and efficient collective behavior emerging in groups of information-seeking agents Ehud D. Karpasa, Adi Shklarsha, and Elad Schneidmana,1 aDepartment of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel Edited by Curtis G. Callan Jr., Princeton University, Princeton, NJ, and approved April 17, 2017 (received for review October 31, 2016) Individual behavior, in biology, economics, and computer science, is highly efficient in finding a sparsely signaling source in a tur- is often described in terms of balancing exploration and exploita- bulent environment. These infotaxis search trajectories resemble tion. Foraging has been a canonical setting for studying reward the paths of foraging insects, suggesting a biological implication seeking and information gathering, from bacteria to humans, of this model. mostly focusing on individual behavior. Inspired by the gradient- In nature, many species, including bacteria (15), amoebae (16), climbing nature of chemotaxis, the infotaxis algorithm showed insects (17, 18), fish (19), birds (3), and mammals (20, 21), dis- that locally maximizing the expected information gain leads to play complex group behavior, including foraging. The mecha- efficient and ethological individual foraging. In nature, as well as nisms that underlie group behavior have been of great experi- in theoretical settings, conspecifics can be a valuable source of mental and theoretical interest, focusing on the computation that information about the environment. Whereas the nature and role each individual performs (22–24) and emergent collective behav- of interactions between animals have been studied extensively, ior (24, 25). In terms of social behavior, such models have been the design principles of information processing in such groups used to describe exploration and exploitation of the environment, are mostly unknown. We present an algorithm for group forag- finding food or mates, decision making (26–29), and altruistic and ing, which we term “socialtaxis,” that unifies infotaxis and social opportunistic behavior, as well as the design of systems of conflict- interactions, where each individual in the group simultaneously ing components (30) and distributed algorithms (31). BIOPHYSICS AND maximizes its own sensory information and a social information We present a model of foraging in a group that combines COMPUTATIONAL BIOLOGY term. Surprisingly, we show that when individuals aim to increase infotaxis and social interactions, using information as a unifying their information diversity, efficient collective behavior emerges principle. In this socialtaxis model, agents seek a signal-emitting in groups of opportunistic agents, which is comparable to the source, using the information they receive through their own optimal group behavior. Importantly, we show the high efficiency “senses” and information they receive from other agents or that of biologically plausible socialtaxis settings, where agents share they infer from the behavior of their conspecifics. We show that little or no information and rely on simple computations to infer certain forms of socialtaxis allow a collection of opportunistic ECOLOGY information from the behavior of their conspecifics. Moreover, individuals to find the source considerably faster than a collection socialtaxis does not require parameter tuning and is highly robust of independent agents and comparable to the case of agents shar- to sensory and behavioral noise. We use socialtaxis to predict dis- ing all their sensory information and decision making using a cen- tinct optimal couplings in groups of selfish vs. altruistic agents, trally managed strategy (which is exponentially more expensive). reflecting how it can be naturally extended to study social dynam- Moreover, we find that coordinated group behavior emerges in a ics and collective computation in general settings. collection of selfish individuals each maximizing their own goal. We further present biologically plausible versions of socialtaxis, foraging j information maximization j chemotaxis j exploration j exploitation Significance From bacteria to humans, individual foraging has been a key oraging is fundamental for survival and reproduction in example of complex behavior, often analyzed experimentally Fnumerous species and is often based on sparse and noisy sen- and theoretically, in terms of a trade-off between exploration sory cues in complex environments. Understanding how organ- and exploitation. Finding a source in a nonturbulent environ- isms represent space and navigate and the utility functions and ment can be done by following the gradient of a signal, but in computations that underlie movement patterns and social behav- noisy environments, moving to maximize information about ior (1–6) critically depends on characterizing the nature of for- the source results in efficient searches. We present a model aging. Theoretical models of foraging have been pivotal in eco- for group foraging, in which each agent aims to maximize nomics, physics (7, 8), and machine learning (9) as a general its own information and minimize its informational overlap framework for decision making, exploration and exploitation, with others. The result is a highly efficient, robust, biologically optimization, and learning (10). plausible, and nearly optimal collective group behavior. This Climbing the gradient of a sensory signal is an efficient forag- suggests information maximization from sensory and social ing strategy for finding a strong source in nonturbulent environ- sources as an optimization principle that can direct individual ments or on a microscopic scale, as demonstrated, for example, and group behavior. by theoretical and experimental studies of bacterial chemotaxis (1, 11). However, for weak sources, or on a macroscopic scale Author contributions: E.D.K., A.S., and E.S. designed research; E.D.K., A.S., and E.S. per- that is characterized by turbulent flows, the signal coming from a formed research; E.D.K. and E.S. analyzed data; and E.D.K. and E.S. wrote the paper. source is typically broken into random, sparse, and disconnected The authors declare no conflict of interest. patches (12). Without a continuous gradient, a different strategy This article is a PNAS Direct Submission. is needed to read and use information from these patches about 1To whom correspondence should be addressed. Email: elad.schneidman@weizmann. the location of the source (13). Vergassola et al. (14) presented ac.il. a foraging algorithm based on maximizing the information that This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. an agent has about the location of a source and showed that it 1073/pnas.1618055114/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1618055114 PNAS Early Edition j 1 of 6 Downloaded by guest on October 6, 2021 in which agents share little or no information, and its robust- by Gi , or how individuals affect one another, and β, the cou- ness to various forms of noise. Finally, we show socialtactic opti- pling strength or inverse “temperature,” which balances individ- mal behaviors in game theory-like settings of competing and ual information and social interactions: β = 0 reduces socialtaxis opportunistic agents, suggesting a wide range of applications for to the standard individual infotaxis behavior of each agent, and this model. β ! 1 implies pure socially driven behavior. Following many models of collective behavior, a natural choice From Individual Infotaxis to Socialtaxis for the relation between individuals would be one that is deter- The infotaxis algorithm (14) describes a strategy for individual mined by the physical distance between them. We consider here foraging in space, where an agent (or animal) moves to maxi- the case where the free energy of agent i is given by mize the information it has about the location of a stationary dist α source that emits signals (or particles) in random directions at Fi = S[Pi ] + βΣj dij ; [2] a low rate. In its discretized version, the search space is divided into “cells,” and the agent estimates at each time t a probability where dij is the Euclidean distance between agents i and j , α > 1 map of the possible locations (r) of the source Pt (r). The entropy is a tunable parameter that determines the scaling of the dis- of the map at time t, given by S [Pt (r)] = −ΣrPt (r) log2Pt (r) tance between agents, and the summation goes over all group (32), measures the uncertainty or missing information about the members. We explored the behavior of groups of 2–20 agents location of the source, in bits. At each time point, the agent may searching for a single sparse source in a 2D arena and found (i) find the source, (ii) detect a signal from the source (“hit”), or that for each choice of α, there was an optimal β that was always (iii) detect nothing. The agent then updates its probability map positive and minimized the time needed for the first member of over the space based on one of these three events and uses the the group to find the source (Distance-Based Socialtaxis). How- new map to decide whether to move to a neighboring cell or stay ever, even for the optimal values, the improvement in search time still. This decision is based on the expected information it would compared with independent agents was very small (more below). gain from each possible move, which is given by the expected Fig. 1B shows an example of the cohesive trajectories of two cou- change in entropy of each of the possible events in that location pled agents with their optimal βopt (Movie S1). (finding the source, getting a hit, or not getting a hit), weighted We then considered a socialtaxis model in which social inter- by the probability of occurrence of each event (Materials and actions were based on the information that agents have and not Methods). Fig. 1A shows the trajectories of two agents who are their physical locations. Here each agent aims to minimize the independently searching the source using infotaxis in a 2D arena, combination of its entropy and the overlap in the information it completely ignoring one another (Movie S1).
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