# Estimation paper

Jordan would say it and substituting appropriate values results in the desired equality. If these assumptions do not hold, then Claxton et al overestimate the success of PCTs in improving health and consequently underestimate the NICE threshold. I am not sure whether the same is true with the undiscounted case as they have here, but it seems like it should since we can set. The first serious difficulty is with the type of data available. Let be the discounted sum of rewards. It is useful because if we are given the form of estimator of the advantage, we can immediately tell if it is an unbiased advantage estimator. Since that problem is partially solved the authors of this paper wanted a function neural network that maximize the mutual information between the given input and the encoded output. Mutual information neural estimation MINE learns a neural estimate of the MI of continuous variables, and it is strongly consistent. Hence we can use MINE to directly measure between input and the feature. When it comes to encoded features, both content as well as independence matters, and the authors trained their function in a similar fashion to AAE to match the statistic properties that they wanted to impose to the encoded features. That update requires an entirely separate optimization procedure. Note I: is not the true value function.

When the encoder does not support infinite output configurations and the feature vector have limited capacity, the encoder must choose what kind of information will be passed on.

The tradeoff here is that the estimators with small have low variance but high bias, whereas those with large have low bias but high variance. We propose an efficient and lightweight encoder-decoder network architecture and apply network pruning to further reduce computational complexity and latency.

### Mutual information neural estimation code

The first serious difficulty is with the type of data available. Stay tuned … Reward Shaping Interpretation Reward shaping originated from a ICML paper, and refers to the technique of transforming the original reward function into a new one via the following transformation with an arbitrary real-valued function on the state space: Amazingly, it was shown that despite how is arbitrary, the reward shaping transformation results in the same optimal policy and optimal policy gradient, at least when the objective is to maximize discounted rewards. Will this work well in practice? Somewhat annoyingly, they use the infinite-horizon setting. A -just estimator of the advantage function results in This is for one time step. They state it clearly: The response function lets us quantify the temporal credit assignment problem: long range dependencies between actions and rewards correspond to nonzero values of the response function for. This paper proposes ways to dramatically reduce variance, but this unfortunately comes at the cost of introducing bias, so one needs to be careful before applying tricks like this in practice. Note II: we also have our policy parameterized by parameters , again typically a neural network.

Suppose is an estimate of the advantage function. Stay tuned … Reward Shaping Interpretation Reward shaping originated from a ICML paper, and refers to the technique of transforming the original reward function into a new one via the following transformation with an arbitrary real-valued function on the state space: Amazingly, it was shown that despite how is arbitrary, the reward shaping transformation results in the same optimal policy and optimal policy gradient, at least when the objective is to maximize discounted rewards.

The authors of this paper were influence by MINE however they found out that it is not necessary to use the exact KL-based formulation as well as to have a generator portion. First, define the temporal difference residual.

This can be done via AAE approach and the objective function will look like below. The combination of and with a policy estimator and a value function estimator is known as the actor-critic model with the policy as the actor and the value function as the critic.

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