Optimality analysis of value-based decisions in binary and multi-alternative choice settings predicts that reaction times should be sensitive only to differences in stimulus magnitudes, but not to overall absolute stimulus magnitude. Yet experimental work in the binary case has shown magnitude sensitive reaction times, and theory shows that this can be explained by switching from linear to multiplicative time costs, but also by nonlinear subjective utility. Thus disentangling explanations for observed magnitude sensitive reaction times is difficult. Here for the first time we extend the theoretical analysis of geometric time-discounting to ternary choices, and present novel experimental evidence for magnitude-sensitivity in such decisions, in both humans and slime moulds. We consider the optimal policies for all possible combinations of linear and geometric time costs, and linear and nonlinear utility; interestingly, geometric discounting emerges as the predominant explanation for magnitude sensitivity.

Social insect colonies use negative as well as positive feedback signals to regulate foraging behaviour. In ants and bees individual foragers have been observed to use negative pheromones or mechano-auditory signals to indicate that forage sources are not ideal, for example being unrewarded, crowded, or dangerous. Here we propose an additional function for negative feedback signals during foraging, variance reduction. We show that while on average populations will converge to desired distributions over forage patches both with and without negative feedback signals, in small populations negative feedback reduces variation around the target distribution compared to the use of positive feedback alone. Our results are independent of the nature of the target distribution, providing it can be achieved by foragers collecting only local information. Since robustness is a key aim for biological systems, and deviation from target foraging distributions may be costly, we argue that this could be a further important and hitherto overlooked reason that negative feedback signals are used by foraging social insects.

Creating a routing backbone is a fundamental problem in both biology and engineering. The routing backbone of the trail networks of arboreal turtle ants (Cephalotes goniodontus) connects many nests and food sources using trail pheromone deposited by ants as they walk. Unlike species that forage on the ground, the trail networks of arboreal ants are constrained by the vegetation. We examined what objectives the trail networks meet by comparing the observed ant trail networks with networks of random, hypothetical trail networks in the same surrounding vegetation and with trails optimized for four objectives: minimizing path length, minimizing average edge length, minimizing number of nodes, and minimizing opportunities to get lost. The ants' trails minimized path length by minimizing the number of nodes traversed rather than choosing short edges. In addition, the ants' trails reduced the opportunity for ants to get lost at each node, favoring nodes with 3D configurations most likely to be reinforced by pheromone. Thus, rather than finding the shortest edges, turtle ant trail networks take advantage of natural variation in the environment to favor coherence, keeping the ants together on the trails.

We investigate decentralised decision-making, in which a robot swarm is tasked with selecting the best-quality option among a set of alternatives. Individual robots are simplistic as they only perform diffusive search, make local noisy estimates of the options' quality, and exchange information with near neighbours. We propose a decentralised algorithm, inspired by house-hunting honeybees, to efficiently aggregate noisy estimations. Individual robots, by varying over time a single decentralised parameter that modulates the interaction strength, balance exploration and agreement. In this way, the swarm first identifies the options under consideration, then rapidly converges on the best available option, even when outnumbered by lower quality options. We present stochastic analyses and swarm robotics simulations to compare the novel strategy with previous methods and to quantify the performance improvement. The proposed strategy limits the spreading of errors within the population and allows swarms of simple noisy units with minimal communication capabilities to make highly accurate collective decisions in predictable time.

Decision making is a complex task, and its underlying mechanisms that regulate behavior, such as the implementation of the coupling between physiological states and neural networks, are hard to decipher. To gain more insight into neural computations underlying ongoing binary decision-making tasks, we consider a neural circuit that guides the feeding behavior of a hypothetical animal making dietary choices. We adopt an inhibition motif from neural network theory and propose a dynamical system characterized by nonlinear feedback, which links mechanism (the implementation of the neural circuit and its coupling to the animal's nutritional state) and function (improving behavioral performance). A central inhibitory unit influences evidence-integrating excitatory units, which in our terms correspond to motivations competing for selection. We determine the parameter regime where the animal exhibits improved decision-making behavior and explain different behavioral outcomes by making the link between accessible states of the nonlinear neural circuit model and decision-making performance. We find that for given deficits in nutritional items, the variation of inhibition strength and ratio of excitation and inhibition strengths in the decision circuit allows the animal to enter an oscillatory phase that describes its internal motivational state. Our findings indicate that this oscillatory phase may improve the overall performance of the animal in an ongoing foraging task and underpin the importance of an integrated functional and mechanistic study of animal activity selection.

The capacity to learn abstract concepts such as 'sameness' and 'difference' is considered a higher-order cognitive function, typically thought to be dependent on top-down neocortical processing. It is therefore surprising that honey bees apparantly have this capacity. Here we report a model of the structures of the honey bee brain that can learn sameness and difference, as well as a range of complex and simple associative learning tasks. Our model is constrained by the known connections and properties of the mushroom body, including the protocerebral tract, and provides a good fit to the learning rates and performances of real bees in all tasks, including learning sameness and difference. The model proposes a novel mechanism for learning the abstract concepts of 'sameness' and 'difference' that is compatible with the insect brain, and is not dependent on top-down or executive control processing.

Flying insects are capable of a wide-range of flight and cognitive behaviors which are not currently understood. The replication of these capabilities is of interest to miniaturized robotics, because they share similar size, weight, and energy constraints. Currently, embodiment of insect behavior is primarily done on ground robots which utilize simplistic sensors and have different constraints to flying insects. This limits how much progress can be made on understanding how biological systems fundamentally work. To address this gap, we have developed an inexpensive robotic solution in the form of a quadcopter aptly named BeeBot. Our work shows that BeeBot can support the necessary payload to replicate the sensing capabilities which are vital to bees' flight navigation, including chemical sensing and a wide visual field-of-view. BeeBot is controlled wirelessly in order to process this sensor data off-board; for example, in neural networks. Our results demonstrate the suitability of the proposed approach for further study of the development of navigation algorithms and of embodiment of insect cognition.

We present a novel neurally based model for estimating angular velocity (AV) in the bee brain, capable of quantitatively reproducing experimental observations of visual odometry and corridor-centering in free-flying honeybees, including previously unaccounted for manipulations of behaviour. The model is fitted using electrophysiological data, and tested using behavioural data. Based on our model we suggest that the AV response can be considered as an evolutionary extension to the optomotor response. The detector is tested behaviourally in silico with the corridor-centering paradigm, where bees navigate down a corridor with gratings (square wave or sinusoidal) on the walls. When combined with an existing flight control algorithm the detector reproduces the invariance of the average flight path to the spatial frequency and contrast of the gratings, including deviations from perfect centering behaviour as found in the real bee's behaviour. In addition, the summed response of the detector to a unit distance movement along the corridor is constant for a large range of grating spatial frequencies, demonstrating that the detector can be used as a visual odometer.

In this paper we present a simple and general new No Free Lunch-like result that applies to revisiting algorithms searching arbitrary problem sets. We begin by unifying the assumptions of closure under permutation and non-revisiting algorithms. We then propose a new approach to reasoning about search algorithm performance, treating search algorithms as stochastic processes and thereby admitting revisiting; for this approach we need only make a simple assumption that search algorithms are applied for optimisation (i.e. maximisation or minimisation), rather than considering arbitrary performance measures. As a consequence of a proof that non-revisiting enumeration has the best possible expected performance for arbitrary distributions over arbitrary problem sets, this allows us to show that better than enumeration performance by some algorithm on some problem set predicts nothing about performance on a second problem set when nothing is known about the relation between the two. Finally we note that enumeration typically has excellent time and space complexities. Our approach is both simple and powerful; our new No Free Lunch-like result is stronger than the originals both in its predictions and, apart from not applying to arbitrary performance measures but only to those reflecting the typical goal of search, weaker than the originals in its assumptions. It is also directly relevant to research into real-world search algorithms.

We present a probabilistic formulation of UCS (a sUpervised Classifier System). UCS is shown to be a special case of mixture of experts where the experts are learned independently and later combined during prediction. In this work, we develop the links between the constituent components of UCS and a mixture of experts, thus lending UCS a strong analytical background. We find during our analysis that mixture of experts is a more generic formulation of UCS and possesses more generalization capability and flexibility than UCS, which is also verified using empirical evaluations. This is the first time that a simple probabilistic model has been proposed for UCS and we believe that this work will form a useful tool to analyse Learning Classifier Systems and gain useful insights into their working.

Credit assignment is a fundamental issue for the Learning Classifier Systems literature. We engage in a detailed investigation of credit assignment in one recent system called UCS, and in the process uncover two previously undocumented features. We draw on techniques from the classical pattern recognition literature, showing how to analytically derive an optimal credit assignment system, given certain assumptions. Our primary aim is not to improve accuracy, but to better understand the system and put it on a more solid theoreticalfoundation. Nonetheless, empirical results on benign data demonstrate our new system, called UCSpv (UCS with principled voting), can match or exceed the original UCS. Further, its fitness function is principled, and, unlike that of UCS, requires no tuning. However, on more difficult data it seems UCSpv does need some form of tuning or correction. We believe the framework we adopt offers a promising new direction for LCS research, providing principled methods for action selection and bringing LCS closer to the mainstream pattern recognition literature.

The representation used by a learning algorithm introduces a bias which is more or less well-suited to any given learning problem. It is well known that, across all possible problems, one algorithm is no better than any other. Accordingly, the traditional approach in machine learning is to choose an appropriate representation making use of some domain-specific knowledge, and this representation is then used exclusively during the learning process.To reduce reliance on domain-knowledge and its appropriate use it would be desirable for the learning algorithm to select its own representation for the problem.We investigate this with XCS, a Michigan-style Learning Classifier System.We begin with an analysis of two representations from the literature: hyperplanes and hyperspheres. We then apply XCS with either one or the other representation to two Boolean functions, the well-known multiplexer function and a function defined by hyperspheres, and confirm that planes are better suited to the multiplexer and spheres to the sphere-based function.Finally, we allow both representations to compete within XCS, which learns the most appropriate representation for problem thanks to the pressure against overlapping rules which its niche GA supplies. The result is an ecology in which the representations are species.

Viscous populations (those whose members are spatially distributed and have limited mobility and locality of interaction and mating) have been proposed to support the evolution of reciprocal cooperation among self-interested individuals. Here we present a model of such a population and describe how its examination yielded the realization that different classes of viscous populations exist with differing levels of support for reciprocal cooperation. Specifically we find from our model that, in a spatially distributed population with increased viscosity, the reciprocally cooperative tit-for-tat strategy may not be globally stable due to a corresponding increase in local population density.