How humans make repeated choices among options with imperfectly known reward outcomes is an important problem in psychology and neuroscience. This is often studied using multi-armed bandits, which is also frequently studied in machine learning. We present data from a human stationary bandit experiment, in which we vary the average abundance and variability of reward availability (mean and variance of reward rate distributions). Surprisingly, we find subjects significantly underestimate prior mean of reward rates -- based on their self-report, at the end of a game, on their reward expectation of non-chosen arms. Previously, human learning in the bandit task was found to be well captured by a Bayesian ideal learning model, the Dynamic Belief Model (DBM), albeit under an incorrect generative assumption of the temporal structure - humans assume reward rates can change over time even though they are actually fixed. We find that the pessimism bias in the bandit task is well captured by the prior mean of DBM when fitted to human choices; but it is poorly captured by the prior mean of the Fixed Belief Model (FBM), an alternative Bayesian model that (correctly) assumes reward rates to be constants. This pessimism bias is also incompletely captured by a simple reinforcement learning model (RL) commonly used in neuroscience and psychology, in terms of fitted initial Q-values. While it seems sub-optimal, and thus mysterious, that humans have an underestimated prior reward expectation, our simulations show that an underestimated prior mean helps to maximize long-term gain, if the observer assumes volatility when reward rates are stable and utilizes a softmax decision policy instead of the optimal one (obtainable by dynamic programming). This raises the intriguing possibility that the brain underestimates reward rates to compensate for the incorrect non-stationarity assumption in the generative model and a simplified decision policy.

Inmultiagent domains, coping withnon-stationary agents thatchange behaviors from time to time is a challenging problem, where an agent is usually required to be able to quickly detect the other agent's policy during online interaction, and then adapt its own policy accordingly.

Second, OBL policies may bebrittle when paired with anoveltest time partner,e.g.

Zero-shot coordination (ZSC) evaluates an algorithm by the performance of a team of agents that were trained independently under that algorithm. Off-belief learning (OBL) is a recent method that achieves state-of-the-art results in ZSC in the game Hanabi. However, the implementation of OBL relies on a belief model that experiences covariate shift. Moreover, during ad-hoc coordination, OBL or any other neural policy may experience test-time covariate shift.

How humans make repeated choices among options with imperfectly known reward outcomes is an important problem in psychology and neuroscience. This is often studied using multi-armed bandits, which is also frequently studied in machine learning. We present data from a human stationary bandit experiment, in which we vary the average abundance and variability of reward availability (mean and variance of reward rate distributions). Surprisingly, we find subjects significantly underestimate prior mean of reward rates -- based on their self-report, at the end of a game, on their reward expectation of non-chosen arms. Previously, human learning in the bandit task was found to be well captured by a Bayesian ideal learning model, the Dynamic Belief Model (DBM), albeit under an incorrect generative assumption of the temporal structure - humans assume reward rates can change over time even though they are actually fixed. We find that the pessimism bias in the bandit task is well captured by the prior mean of DBM when fitted to human choices; but it is poorly captured by the prior mean of the Fixed Belief Model (FBM), an alternative Bayesian model that (correctly) assumes reward rates to be constants. This pessimism bias is also incompletely captured by a simple reinforcement learning model (RL) commonly used in neuroscience and psychology, in terms of fitted initial Q-values. While it seems sub-optimal, and thus mysterious, that humans have an underestimated prior reward expectation, our simulations show that an underestimated prior mean helps to maximize long-term gain, if the observer assumes volatility when reward rates are stable and utilizes a softmax decision policy instead of the optimal one (obtainable by dynamic programming). This raises the intriguing possibility that the brain underestimates reward rates to compensate for the incorrect non-stationarity assumption in the generative model and a simplified decision policy.

There also exist many application scenarios involving multiagent interactions, commonly known as multiagent systems (MAS).

It has been found that DBM captures human behavior better than FBM, even though the latter more veridically captures experimental design in a variety of tasks, e.g.

It has been found that DBM captures human behavior better than FBM, even though the latter more veridically captures experimental design in a variety of tasks, e.g.

We dynamically batch model calls onto the GPU in order to increase inference speed. For OBL, there are dependencies between policy and belief training. The entire inference and training infrastructure for a single policy or belief model uses a machine with 30 CPU cores and 2 GPUs, one GPU for training and one for simulation. We use their public-lstm architecture design. We use a 3-layer feedforward neural network to encode the entire private observation.