function [V] = eg_7_5_learn_at(lambda,alpha,n_rw_states,nEpisodes)
% EG_7_5_LEARN_AT - Performs td(lambda) learning with {\em accumulating} eligibility traces
% 
% Written by:
% -- 
% John L. Weatherwax                2007-12-07
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% the number of episodes (in general this would need to be much larger to gaureentee complete learning):
%nEpisodes = 1000; 

% the number of non terminal states plus the one terminal states: 
nStates=n_rw_states+1;

% initialize the states ... terminal states are defined to be ZERO 
V = zeros(1,nStates); 

% initialize the eligbility trace (to zero):
et = zeros(1,nStates);

%gamma     = 1.0; 
gamma     = 0.9; 

for ei=1:nEpisodes,
  
  % perform a random walk getting the sequence of rewards recieved and the 
  % sequence of states we transition through ... this is the surragate of
  % performing actions with some policy 
  % 
  [rewseen,stateseen] = eg_7_5_episode(n_rw_states); 
  
  % compute the temporal difference and elibility traces update for each 
  % state s_t for t=0,1,2,\cdots,T-1 (the states visited)
  % 
  % and use these to update V(\cdot):
  % 
  T = length(rewseen); 
  for t=0:(T-1),    % <- STATE index ... 
    
    st     = stateseen(t+1);    
    rew    = rewseen(t+1); 
    stp    = stateseen(t+2); 
    delta  = rew + gamma*V(stp) - V(st); % the temporal difference
    % implement UPDATING elagability traces:
    et(st) = et(st)+1;  

    % update V(\cdot) with this information: 
    V = V + alpha*delta*et;
    % decay our elibility trace:
    et = gamma*lambda*et; 
    
  end % end state sequence loop ... 
  
end % end episode loop ... 

% remove the terminal states: 
V = V(1:end-1);