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Cass Sunstein

May-June 1998

Kenneth Starr's behavior as independent counsel follows a pattern set in other investigations: the problem lies in the incentives and unchecked power of the office.

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T he institutional design of the Independent Counsel is designed to heighten, not to check, all of the institutional hazards of the dedicated prosecutor; the danger of too narrow a focus, of the loss of perspective, of preoccupation with the pursuit of one alleged suspect to the exclusion of other interests." Thus wrote Supreme Court Justice Antonin Scalia nearly a decade ago, echoing the warning of three attorneys general, two of them staunch Republicans. In his dissenting vote to hold the Independent Counsel Act unconstitutional, Scalia objected that the supposedly independent counsel is a novel and dangerous means of law enforcement: a prosecutor who is effectively accountable to no one and entirely focused on a single person.

Kenneth Starr was appointed to investigate possible illegality in connection with the Whitewater affair in Arkansas. Nearly four years and $30 million later, Starr authorized and obtained tape recordings of private conversations with Monica Lewinsky, the former White House aide. As of this writing he has also threatened criminal charges against Lewinsky, issued subpoenas to a large number of people who may have talked to Lewinsky about her sex life, forced Lewinsky's own mother through two days of testimony before a grand jury, and sought testimony from members of the Secret Service and from Lewinsky's original lawyer. Whatever may be the outcome of this investigation—whatever its fate or that of President Clinton—it cannot be doubted that Starr's behavior extends far beyond the usual practice of the criminal prosecutor. Prosecutors do not ordinarily authorize tape recordings designed to capture private accounts of alleged illicit sexual relations, and they rarely threaten to bring perjury charges as a result of affidavits in civil cases, especially when the affidavits involve such relations.

This article is not primarily about Starr's investigation. What is remarkable is that Starr's conduct has been paralleled by a large number of less publicized but drawn-out, expensive, and sometimes obsessive investigations by other independent prosecutors. The peculiar behavior is best understood as a product of the bizarre incentives created by the Independent Counsel Act, one of the most ill-conceived pieces of legislation in the last quarter century.

state S0 Environment state S0, action A0 state S1 reward R1 at the end of the episode maximum expected future reward the rewards at each step

Let’s take an example:

If we take the maze environment:

By running more and more episodes, the agent will learn to play better and better.

Temporal Difference Learning: learning at each timestep

TD Learning, on the other hand, will not wait until the end of the episode to update the maximum expected future reward estimation: it will update its value estimation V for the non-terminal states St occurring at that experience.

This method is called TD(0) or one step TD (update the value function after any individual step).

TD methods only wait until the next time step to update the value estimates. At time t+1 they immediately form a TD target using the observed reward Rt+1 and the current estimate V(St+1).

TD target is an estimation: in fact you update the previous estimate V(St) by updating it towards a one-step target.

Exploration/Exploitation tradeoff

Before looking at the different strategies to solve Reinforcement Learning problems, we must cover one more very important topic: the exploration/exploitation trade-off.

Remember, the goal of our RL agent is to maximize the expected cumulative reward. However, we can fall into a common trap.

In this game, our mouse can have an infinite amount of small cheese (+1 each). But at the top of the maze there is a gigantic sum of cheese (+1000).

However, if we only focus on reward, our agent will never reach the gigantic sum of cheese. Instead, it will only exploit the nearest source of rewards, even if this source is small (exploitation).

But if our agent does a little bit of exploration, it can find the big reward.

This is what we call the exploration/exploitation trade off. We must define a rule that helps to handle this trade-off.We’ll see in future articles different ways to handle it.

Three approaches to Reinforcement Learning

Now that we defined the main elements of Reinforcement Learning, let’s move on to the three approaches to solve a Reinforcement Learning problem. These are value-based, policy-based, and model-based.

Value Based

In value-based RL, the goal is to optimize the value function .

The value function is a function that tells us the maximum expected future reward the agent will get at each state.

The value of each state is the total amount of the reward an agent can expect to accumulate over the future, starting at that state.

The agent will use this value function to select which state to choose at each step. The agent takes the state with the biggest value.

In the maze example, at each step we will take the biggest value: -7, then -6, then -5 (and so on) to attain the goal.

Policy Based

In policy-based RL, we want to directly optimize the policy function without using a value function.

The policy is what defines the agent behavior at a given time.

We learn a policy function. This lets us map each state to the best corresponding action.

We have two types of policy:

As we can see here, the policy directly indicates the best action to take for each steps.

Model Based

In model-based RL, we model the environment. This means we create a model of the behavior of the environment.

The problem is each environment will need a different model representation. That’s why we will not speak about this type of Reinforcement Learning in the upcoming articles.

Introducing Deep Reinforcement Learning

Deep Reinforcement Learning introduces deep neural networks to solve Reinforcement Learning problems — hence the name “deep.”

For instance, in the next article we’ll work on Q-Learning (classic Reinforcement Learning) and Deep Q-Learning.

You’ll see the difference is that in the first approach, we use a traditional algorithm to create a Q table that helps us find what action to take for each state.

In the second approach, we will use a Neural Network (to approximate the reward based on state: q value).

Congrats! There was a lot of information in this article. Be sure to really grasp the material before continuing. It’s important to master these elements before entering the fun part: creating AI that plays video games.

Important: t his article is the first part of a free series of blog posts about Deep Reinforcement Learning. For more information and more resources, check out the syllabus.

Next time we’ll work on a Q-learning agent that learns to play the Frozen Lake game.

If you have any thoughts, comments, questions, feel free to comment below or send me an email: hello@simoninithomas.com, or tweet me @ThomasSimonini .

If you liked my article, please click the 👏 below as many time as you liked the article so other people will see this here on Medium. And don’t forget to follow me!

Cheers!

Deep Reinforcement LearningCourse:

Part 4: An introduction to Policy Gradients with Doom and Cartpole

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