8 votes
Accepted

How to show temporal difference methods converge to MLE?

The convergence and optimality proofs of (linear) temporal-difference methods (under batch training, so not online learning) can be found in the paper Learning to predict by the methods of temporal ...
  • 35.6k
6 votes

What is convergence in machine learning?

When formulating a problem in deep learning, we need to come up with a loss function, which uses model weights as parameters. Back-propagation starts at an arbitrary point on the error manifold ...
  • 1,369
6 votes
Accepted

What are the conditions of convergence of temporal-difference learning?

There are different TD algorithms, e.g. Q-learning and SARSA, whose convergence properties have been studied separately (in many cases). In some convergence proofs, e.g. in the paper Convergence of ...
  • 35.6k
5 votes

Why can the Bellman equation be turned into an update rule?

Why are we allowed to convert the Bellman equations into update rules? There is a simple reason for this: convergence. The same chapter 4 of the same book mentions it. For example, in the case of ...
  • 35.6k
5 votes
Accepted

Deep Q-Learning poor convergence on Stochastic Environment

The inputs that you describe seem like they should be sufficient for a DQN-based agent to learn a good strategy for playing Minesweeper, regardless of whether or not the starting layout changes. The ...
  • 9,604
5 votes
Accepted

How can I ensure convergence of DDQN, if the true Q-values for different actions in the same state are very close?

Let $Q^*(s, a)$ denote the "true" $Q$-value for a state-action pair $(s, a)$, i.e. the values that we're hoping to learn to approximate using a neural network that outputs $Q(s, a)$ values. The ...
  • 9,604
5 votes
Accepted

When do SARSA and Q-Learning converge to optimal Q values?

The true answers are 1 and 3. 1 is true because the required conditions for tabular Q-learning to converge is that each state action pair will be visited infinitely often, and Q-learning learns ...
5 votes
Accepted

If $\alpha$ decreases over time, why is Q-learning guaranteed to converge?

Why is this a convergence criterion? It is because $R$ and $S'$ are stochastic. A large learning rate applied when these values have variance would not converge to mean, but would wander around ...
5 votes
Accepted

Why does Q-learning converge under 100% exploration rate?

Q-learning is guaranteed to converge (in the tabular case) under some mild conditions, one of which is that in the limit we visit each state-action tuple infinitely many times. If your random random ...
4 votes
Accepted

How fast does Monte Carlo tree search converge?

Yes, Monte Carlo tree search (MCTS) has been proven to converge to optimal solutions, under assumptions of infinite memory and computation time. That is, at least for the case of perfect-information, ...
  • 9,604
4 votes
Accepted

If deep Q-learning starts to choose only one action, is this a sign that the algorithm diverged?

Is this a sign that the algorithm diverged? It is a common sign of a problem with learning process. That includes divergence due to poor hyper-parameters, even just bad luck. But it can also point to ...
4 votes

How to determine if Q-learning has converged in practice?

A typical and practical way to measure the convergence to some solution (so not necessarily the optimal one!) of any numerical iterative algorithm (such as RL algorithms) is to check if the current ...
  • 35.6k
4 votes

Learning an identity function with convolutional networks

Learning the identity function is not trivial at all. The main reason is that the identity function is linear, and a neural network try to approximate it in a non linear fashion. Non linear ...
3 votes

Is there a simple proof of the convergence of TD(0)?

As far as I know, there is no very simple proof of the convergence of temporal-difference algorithms. The proofs of convergence of TD algorithms are often based on stochastic approximation theory (...
  • 35.6k
3 votes

How is the actor-critic algorithm guaranteed to converge?

There are different actor-critic (AC) algorithms with different convergence guarantees. For example, AC algorithms where the critic is tabular have different convergence guarantees than AC algorithms ...
  • 35.6k
3 votes
Accepted

LSTM network doesn't converge, what should be changed?

writing here my suggestion, because i haven't earned the right to comment yet. Your main "problem" could be your loss function. It converges, this is why your loss value is decreasing. So I suggest ...
  • 146
3 votes

Is there a rigorous proof for finding Hopfield minima?

See the paper On the Convergence Properties of the Hopfield Model (1990), by Jehoshua Bruck. In the first section of the paper, J. Bruck describes the Hopfield network (popularized by J. J. Hopfield ...
  • 35.6k
3 votes
Accepted

Is a calculus or ML approach to varying learning rate as a function of loss and epoch been investigated?

Has this been done? Difficult to prove a negative, but I suspect although plenty of research has been done into finding ideal learning rate values (the need for learning rate at all is an annoyance), ...
3 votes

What is convergence analysis, and why is it needed in reinforcement learning?

Convergence analysis is about proving that your policy and/or value function converge to some desired value, which is usually the fixed-point of an operator or an extremum. So it essentially proves ...
  • 1,051
3 votes

Does the policy iteration convergence hold for finite-horizon MDP?

In the discussion about Neil Slater's answer (that he, sadly, deleted) it was pointed out that the policy $\pi$ should also depend on the horizon $h$. The decision of action $a$ can be influenced by ...
  • 1,923
3 votes

Does elitism cause premature convergence in genetic algorithms?

There are many ideas to escape from local optima in GA. One solution is selecting the population for the next iteration based on the probability that is defined based on the individual score. In that ...
  • 1,703
2 votes

What is chaotic behavior and how it is achieved in non-linear regression and artificial networks?

It looks like you have some common misconceptions about AI and neural networks. First, AI programs generally do not try to imitate the human behaviour of a human brain. Instead, they try to imitate ...
2 votes
Accepted

Which is more important, doubt or reinforcement?

Which is more important, doubt or reinforcement? The single-sentence answer to this would be: it depends. The core of this question seems to be very closely related to the well-known trade-off ...
  • 9,604
2 votes
Accepted

How to create and train (with mutation and selection) a neural network to predict the next state of a board?

Re: Should I also have it randomly delete nodes and connections, in case they also make improvements? You may read about "dropout". In this case it's not preferred since overfitting is actually a ...
  • 286
2 votes

What are the differences between stability and convergence in reinforcement learning?

Sometimes when training, particularly in reinforcement learning, the model can become unstable due to the amount of variance that exists in the training data that the agent generates by interacting ...
  • 393
2 votes

Convergence of semi-gradient TD(0) with non-linear function approximation

Apparently there is an example of non-convergence for semi-gradient sarsa, according to Rich Sutton (check slide 35). I guess TD(0) is not so different. So, probably your approximator will need to ...
2 votes
Accepted

How do we know that the algorithm has converged and ensures the highest possible reward?

Your Q learning update expression looks correct. The Total Reward will not be the same at the end of each episode because the starting position of taxi is different ...
  • 2,286
2 votes

Why does reinforcement learning using a non-linear function approximator diverge when using strongly correlated data as input?

It is not so much the problem of using Reinforcement Learning to train the neural networks, it is the assumptions made about the data given to standard Neural Networks. They are not capable of ...

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