multiRL

Overview

This package modularizes the Markov Decision Process (MDP) into six core components, enabling users to flexibly construct the Rescorla-Wagner Model for Multi-Armed Bandit tasks (see Sutton & Barto, 2018). Beginners can define models using simple if-else logic, making model construction more accessible (built-in three basic models, see Niv et al., 2012).

• Step 1: Build Reinforcement Learning Models run_m()
• Step 2: Parameter and Model Recovery rcv_d()
• Step 3: Fit Real Data fit_p()
• Step 4: Replay the Experiment rpl_e()

These four steps follow the ten simple rules for the computational modeling of behavioral data (Wilson & Collins 2019)

Installation

# Install the stable version from CRAN  
install.packages("multiRL")
# Install the latest version from GitHub
remotes::install_github("yuki-961004/multiRL@*release")

# Load package
library(multiRL)
# Obtain help document
?binaryRL

Markov Decision Process

# learning-rate 
binaryRL::func_eta              -->             multiRL::func_alpha

\[ Q_{new} = Q_{old} + \alpha \cdot (R - Q_{old}) \]

# soft-max  
binaryRL::func_tau              -->             multiRL::func_beta

\[ P_{t}(a) = \frac{ \exp\left( \beta \cdot \left( Q_t(a) - \max_{j} Q_t(a_j) \right) \right) }{ \sum_{i=1}^{k} \exp\left( \beta \cdot \left( Q_t(a_i) - \max_{j} Q_t(a_j) \right) \right ) } \]

# utility function
binaryRL::func_gamma            -->             multiRL::func_gamma

\[ U(R) = {R}^{\gamma} \]

# upper-confidence-bound
binaryRL::func_pi               -->             multiRL::func_delta

\[ \text{Bias} = \delta \cdot \sqrt{\frac{\log(N + e)}{N + 10^{-10}}} \]

# ε-(first, greedy, decrasing)  
binaryRL::func_epsilon          -->             multiRL::func_epsilon

\[ P(x) = \begin{cases} \epsilon, & x=1 \\ 1-\epsilon, & x=0 \end{cases} \]

# working memory system
                                [+]             multiRL::func_zeta

\[ W_{new} = W_{old} + \zeta \cdot (W_{0} - W_{old}) \]

Latent Rules Learning

Sometimes, you do not know what humans treat as the target when they encounter a particular state and update their values, especially when the cue and the response are not the same. In such cases, the agent typically needs to learn latent rules.

behrule = list(
  cue = c("Red", "Yellow", "Green", "Blue"),
  rsp = c("Up", "Down", "Left", "Right")
)

Reference

• Sutton, R. S., & Barto, A. G. (2018). Reinforcement Learning: An Introduction (2nd ed). MIT press.
  
• Wilson, R. C., & Collins, A. G. (2019). Ten simple rules for the computational modeling of behavioral data. Elife, 8, e49547. https://doi.org/10.7554/eLife.49547
  
• Niv, Y., Edlund, J. A., Dayan, P., & O’Doherty, J. P. (2012). Neural prediction errors reveal a risk-sensitive reinforcement-learning process in the human brain. Journal of Neuroscience, 32(2), 551-562. https://doi.org/10.1523/JNEUROSCI.5498-10.2012
  
• Collins, A. G., & Frank, M. J. (2012). How much of reinforcement learning is working memory, not reinforcement learning? A behavioral, computational, and neurogenetic analysis. European Journal of Neuroscience, 35(7), 1024-1035. https://doi.org/10.1111/j.1460-9568.2011.07980.x
  
• Eckstein, M. K., & Collins, A. G. (2020). Computational evidence for hierarchically structured reinforcement learning in humans. Proceedings of the National Academy of Sciences, 117(47), 29381-29389. https://doi.org/10.1073/pnas.1912330117