From 269a75fef9ec4ccecfa4cab3fc8a64b8d9058f29 Mon Sep 17 00:00:00 2001 From: noamgoldway Date: Thu, 16 Sep 2021 15:28:08 -0400 Subject: [PATCH 1/2] Create LearningRateandSoftmax.mlx --- SectionB/LearningRateandSoftmax.mlx | 201 ++++++++++++++++++++++++++++ 1 file changed, 201 insertions(+) create mode 100644 SectionB/LearningRateandSoftmax.mlx diff --git a/SectionB/LearningRateandSoftmax.mlx b/SectionB/LearningRateandSoftmax.mlx new file mode 100644 index 0000000..4626bce --- /dev/null +++ b/SectionB/LearningRateandSoftmax.mlx @@ -0,0 +1,201 @@ +Code and Figures for Section B: How to develop a computational model +How should we choose? +clear; close all; clc +dir ='C:\Users\dream\OneDrive - University College London\Lab\FLUX\2021FluxCompModellingWorkshop-main' +cd(dir); +addpath('.\general_functions\') % add softmax function here + + + +outcome = 1; V = .5; alpha = .6; +PE = outcome - V +V = V + alpha * PE +When reward probabilities are fixed, what is the best learning rate? +% 80:20 rewarding outcomes +outcomes = [zeros(20,1); ones(80,1)]; outcomes = outcomes(randperm(length(outcomes))); + +p_reward =[]; + +p_reward(1:100)= 0.8; + + +% prior at 0 +V = 0.5; +% learning rate +params = []; +params.alpha = 1; %play with this paramenter: try .3, .1 +PE = []; +for t = 1:length(outcomes) + [V(t+1), PE(t)] = learn_RescWagn(V(t),outcomes(t),params); +end + +figure() +plot(V,'DisplayName','value','LineWidth',5) +hold on + +plot(outcomes,'o','DisplayName','outcomes','MarkerSize',48,'Marker','.',... + 'LineStyle','none',... + 'Color',[0.929411764705882 0.694117647058824 0.125490196078431]) +hold on +plot(p_reward,'DisplayName','p(reward)','LineWidth',5,'Color', [0.6350, 0.0780, 0.1840]) + +xlabel('trial','FontSize', 24); +legend('FontSize', 22) + +When reward probabilities are alternating, what is the best learning rate? + +% alternating 80:20 rewarding outcomes +outcomes1 = [zeros(5,1); ones(20,1)]; outcomes1 = outcomes1(randperm(length(outcomes1))); +outcomes2 = [zeros(20,1); ones(5,1)]; outcomes2 = outcomes2(randperm(length(outcomes2))); + +outcomes=[] +outcomes(1:25)=outcomes1 +outcomes(26:50)=outcomes2 +outcomes(51:75)=outcomes1 +outcomes(76:100)=outcomes2 + + +p_reward =[]; + +p_reward(1:25)= 0.8; +p_reward(26:50)= 0.2; +p_reward(51:75)= 0.8; +p_reward(76:100)= 0.2; + + +% learning rate +params = []; +params.alpha = .3; % try .1 +PE = []; +for t = 1:length(outcomes) + [V(t+1), PE(t)] = learn_RescWagn(V(t),outcomes(t),params); +end + +figure() +plot(V,'DisplayName','value','LineWidth',5) +hold on +plot(outcomes,'o','DisplayName','outcomes','MarkerSize',48,'Marker','.',... + 'LineStyle','none',... + 'Color',[0.929411764705882 0.694117647058824 0.125490196078431]) +hold on +plot(p_reward,'DisplayName','p(reward)','LineWidth',5,'Color', [0.6350, 0.0780, 0.1840]) + +xlabel('trial','FontSize', 24); +legend('FontSize', 22) + + + + + +How does the softmax work? +% Value of both purple (1) and orange (2) slot machines ranging from 0 and 100 +values = [0:100; 100:-1:0]; + +Explotiation behaviour - where we choose the slot machine whenever its value is better than the other +Temperature is LOW, choices are LESS NOISY, and more DETERMINSITIC +taus = 0.0001; + +figure() +for i = 1:length(taus) + params = []; params.tau = taus(i); + for v = 1:length(values) + policy(i,v,:) = softmax(values(:,v),params); + end + plot(values(1,:)-values(2,:),squeeze(policy(i,:,1)),'DisplayName',['tau = ' num2str(taus(i))],'LineWidth',2) + hold on +end + +legend +ax = gca; +ax.FontSize = 16; +xlabel('Value (Purple - Orange)','FontSize',20) +ylabel('P(Choose Purple)','FontSize',20) +xlim([-100 100]) +ylim([0 1]) + + +Exploration behaviour - where we choose the slot machines randomly +Temperature is HIGH, choices are MORE NOISY, and more RANDOM +taus = [10000]; + +figure() +for i = 1:length(taus) + params = []; params.tau = taus(i); + for v = 1:length(values) + policy(i,v,:) = softmax(values(:,v),params); + end + plot(values(1,:)-values(2,:),squeeze(policy(i,:,1)),'DisplayName',['tau = ' num2str(taus(i))],'LineWidth',2) + hold on +end +legend +ax = gca; +ax.FontSize = 16; +xlabel('Value (Purple - Orange)','FontSize',20) +ylabel('P(Choose Purple)','FontSize',20) +xlim([-100 100]) +ylim([0 1]) + + + +Varying temperature leads to different choice curves.... +taus = [0.01; 15; 1000]; + +figure() +for i = 1:length(taus) + params = []; params.tau = taus(i); + for v = 1:length(values) + policy(i,v,:) = softmax(values(:,v),params); + end + plot(values(1,:)-values(2,:),squeeze(policy(i,:,1)),'DisplayName',['tau = ' num2str(taus(i))],'LineWidth',2) + hold on +end +legend +ax = gca; +ax.FontSize = 16; +xlabel('Value (Purple - Orange)','FontSize',20) +ylabel('P(Choose Purple)','FontSize',20) +xlim([-100 100]) +ylim([0 1]) + + + +When temperature = 1, +taus = [1]; + +figure() +for i = 1:length(taus) + params = []; params.tau = taus(i); + for v = 1:length(values) + policy(i,v,:) = softmax(values(:,v),params); + end + plot(values(1,:)-values(2,:),squeeze(policy(i,:,1)),'DisplayName',['tau = ' num2str(taus(i))],'LineWidth',2, 'Color','b') + hold on +end +legend +ax = gca; +ax.FontSize = 16; +xlabel('Value (Purple - Orange)','FontSize',20) +ylabel('P(Choose Purple)','FontSize',20) +xlim([-100 100]) +ylim([0 1]) + + +When temperature = 15, +taus = [15]; + +figure() +for i = 1:length(taus) + params = []; params.tau = taus(i); + for v = 1:length(values) + policy(i,v,:) = softmax(values(:,v),params); + end + plot(values(1,:)-values(2,:),squeeze(policy(i,:,1)),'DisplayName',['tau = ' num2str(taus(i))],'LineWidth',2, 'Color','r') + hold on +end +legend +ax = gca; +ax.FontSize = 16; +xlabel('Value (Purple - Orange)','FontSize',20) +ylabel('P(Choose Purple)','FontSize',20) +xlim([-100 100]) +ylim([0 1]) From a53cbd2c2f7394795db3462edc70a26f722c9900 Mon Sep 17 00:00:00 2001 From: noamgoldway Date: Thu, 16 Sep 2021 15:30:06 -0400 Subject: [PATCH 2/2] Add files via upload --- 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