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position: relative; z-index: 10;"><div class="inline-flex rounded-md max-sm:rounded-sm"><button class="inline-flex items-center gap-1 max-sm:gap-0.5 h-6 max-sm:h-5 px-2 max-sm:px-1.5 text-[11px] max-sm:text-[9px] font-medium text-gray-800 border border-r-0 rounded-l-md max-sm:rounded-l-sm border-gray-200 bg-white hover:shadow-inner dark:border-gray-850 dark:bg-gray-950 dark:text-gray-200 dark:hover:bg-gray-800" aria-live="polite"><span class="inline-flex items-center justify-center rounded-md p-0.5 max-sm:p-0"><svg class="w-3 h-3 max-sm:w-2.5 max-sm:h-2.5" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" fill="currentColor" focusable="false" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 32 32"><path d="M28,10V28H10V10H28m0-2H10a2,2,0,0,0-2,2V28a2,2,0,0,0,2,2H28a2,2,0,0,0,2-2V10a2,2,0,0,0-2-2Z" transform="translate(0)"></path><path d="M4,18H2V4A2,2,0,0,1,4,2H18V4H4Z" transform="translate(0)"></path><rect fill="none" width="32" height="32"></rect></svg></span> <span>Copy page</span></button> <button class="inline-flex items-center justify-center w-6 max-sm:w-5 h-6 max-sm:h-5 disabled:pointer-events-none text-sm text-gray-500 hover:text-gray-700 dark:hover:text-white rounded-r-md max-sm:rounded-r-sm border border-l transition border-gray-200 bg-white hover:shadow-inner dark:border-gray-850 dark:bg-gray-950 dark:text-gray-200 dark:hover:bg-gray-800" aria-haspopup="menu" aria-expanded="false" aria-label="Open copy menu"><svg class="transition-transform text-gray-400 overflow-visible w-3 h-3 max-sm:w-2.5 max-sm:h-2.5 rotate-0" width="1em" height="1em" viewBox="0 0 12 7" fill="none" xmlns="http://www.w3.org/2000/svg"><path d="M1 1L6 6L11 1" stroke="currentColor"></path></svg></button></div> </div>  <h1 class="relative group"><a id="two-methods" class="header-link block pr-1.5 text-lg no-hover:hidden with-hover:absolute with-hover:p-1.5 with-hover:opacity-0 with-hover:group-hover:opacity-100 with-hover:right-full" href="#two-methods"><span><svg class="" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 256 256"><path d="M167.594 88.393a8.001 8.001 0 0 1 0 11.314l-67.882 67.882a8 8 0 1 1-11.314-11.315l67.882-67.881a8.003 8.003 0 0 1 11.314 0zm-28.287 84.86l-28.284 28.284a40 40 0 0 1-56.567-56.567l28.284-28.284a8 8 0 0 0-11.315-11.315l-28.284 28.284a56 56 0 0 0 79.196 79.197l28.285-28.285a8 8 0 1 0-11.315-11.314zM212.852 43.14a56.002 56.002 0 0 0-79.196 0l-28.284 28.284a8 8 0 1 0 11.314 11.314l28.284-28.284a40 40 0 0 1 56.568 56.567l-28.285 28.285a8 8 0 0 0 11.315 11.314l28.284-28.284a56.065 56.065 0 0 0 0-79.196z" fill="currentColor"></path></svg></span></a> <span>Two main approaches for solving RL problems</span></h1> <blockquote class="tip">Now that we learned the RL framework, how do we solve the RL problem?</blockquote> <p data-svelte-h="svelte-1poqzkt">In other words, how do we build an RL agent that can <strong>select the actions that maximize its expected cumulative reward?</strong></p>  <h2 class="relative group"><a id="policy" class="header-link block pr-1.5 text-lg no-hover:hidden with-hover:absolute with-hover:p-1.5 with-hover:opacity-0 with-hover:group-hover:opacity-100 with-hover:right-full" href="#policy"><span><svg class="" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 256 256"><path d="M167.594 88.393a8.001 8.001 0 0 1 0 11.314l-67.882 67.882a8 8 0 1 1-11.314-11.315l67.882-67.881a8.003 8.003 0 0 1 11.314 0zm-28.287 84.86l-28.284 28.284a40 40 0 0 1-56.567-56.567l28.284-28.284a8 8 0 0 0-11.315-11.315l-28.284 28.284a56 56 0 0 0 79.196 79.197l28.285-28.285a8 8 0 1 0-11.315-11.314zM212.852 43.14a56.002 56.002 0 0 0-79.196 0l-28.284 28.284a8 8 0 1 0 11.314 11.314l28.284-28.284a40 40 0 0 1 56.568 56.567l-28.285 28.285a8 8 0 0 0 11.315 11.314l28.284-28.284a56.065 56.065 0 0 0 0-79.196z" fill="currentColor"></path></svg></span></a> <span>The Policy π: the agent’s brain</span></h2> <p data-svelte-h="svelte-1sury9w">The Policy <strong>π</strong> is the <strong>brain of our Agent</strong>, it’s the function that tells us what <strong>action to take given the state we are in.</strong> So it <strong>defines the agent’s behavior</strong> at a given time.</p> <figure data-svelte-h="svelte-wr9ae2"><img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit1/policy_1.jpg" alt="Policy"> <figcaption>Think of policy as the brain of our agent, the function that will tell us the action to take given a state</figcaption></figure> <p data-svelte-h="svelte-g271gb">This Policy <strong>is the function we want to learn</strong>, our goal is to find the optimal policy π*, the policy that <strong>maximizes expected return</strong> when the agent acts according to it. We find this π* <strong>through training.</strong></p> <p data-svelte-h="svelte-7rf0mi">There are two approaches to train our agent to find this optimal policy π*:</p> <ul data-svelte-h="svelte-1dvt8p7"><li><strong>Directly,</strong> by teaching the agent to learn which <strong>action to take,</strong> given the current state: <strong>Policy-Based Methods.</strong></li> <li>Indirectly, <strong>teach the agent to learn which state is more valuable</strong> and then take the action that <strong>leads to the more valuable states</strong>: Value-Based Methods.</li></ul>  <h2 class="relative group"><a id="policy-based" class="header-link block pr-1.5 text-lg no-hover:hidden with-hover:absolute with-hover:p-1.5 with-hover:opacity-0 with-hover:group-hover:opacity-100 with-hover:right-full" href="#policy-based"><span><svg class="" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 256 256"><path d="M167.594 88.393a8.001 8.001 0 0 1 0 11.314l-67.882 67.882a8 8 0 1 1-11.314-11.315l67.882-67.881a8.003 8.003 0 0 1 11.314 0zm-28.287 84.86l-28.284 28.284a40 40 0 0 1-56.567-56.567l28.284-28.284a8 8 0 0 0-11.315-11.315l-28.284 28.284a56 56 0 0 0 79.196 79.197l28.285-28.285a8 8 0 1 0-11.315-11.314zM212.852 43.14a56.002 56.002 0 0 0-79.196 0l-28.284 28.284a8 8 0 1 0 11.314 11.314l28.284-28.284a40 40 0 0 1 56.568 56.567l-28.285 28.285a8 8 0 0 0 11.315 11.314l28.284-28.284a56.065 56.065 0 0 0 0-79.196z" fill="currentColor"></path></svg></span></a> <span>Policy-Based Methods</span></h2> <p data-svelte-h="svelte-4zn9b3">In Policy-Based methods, <strong>we learn a policy function directly.</strong></p> <p data-svelte-h="svelte-oozyd0">This function will define a mapping from each state to the best corresponding action. Alternatively, it could define <strong>a probability distribution over the set of possible actions at that state.</strong></p> <figure data-svelte-h="svelte-1m4eqa9"><img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit1/policy_2.jpg" alt="Policy"> <figcaption>As we can see here, the policy (deterministic) <b>directly indicates the action to take for each step.</b></figcaption></figure> <p data-svelte-h="svelte-119iy72">We have two types of policies:</p> <ul data-svelte-h="svelte-h86bbg"><li><em>Deterministic</em>: a policy at a given state <strong>will always return the same action.</strong></li></ul> <figure data-svelte-h="svelte-15macrs"><img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit1/policy_3.jpg" alt="Policy"> <figcaption>action = policy(state)</figcaption></figure> <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit1/policy_4.jpg" alt="Policy" width="100%"> <ul data-svelte-h="svelte-1q48317"><li><em>Stochastic</em>: outputs <strong>a probability distribution over actions.</strong></li></ul> <figure data-svelte-h="svelte-dxiuol"><img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit1/policy_5.jpg" alt="Policy"> <figcaption>policy(actions | state) = probability distribution over the set of actions given the current state</figcaption></figure> <figure data-svelte-h="svelte-120mc27"><img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit1/policy-based.png" alt="Policy Based"> <figcaption>Given an initial state, our stochastic policy will output probability distributions over the possible actions at that state.</figcaption></figure> <p data-svelte-h="svelte-1uwte4">If we recap:</p> <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit1/pbm_1.jpg" alt="Pbm recap" width="100%"> <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit1/pbm_2.jpg" alt="Pbm recap" width="100%">  <h2 class="relative group"><a id="value-based" class="header-link block pr-1.5 text-lg no-hover:hidden with-hover:absolute with-hover:p-1.5 with-hover:opacity-0 with-hover:group-hover:opacity-100 with-hover:right-full" href="#value-based"><span><svg class="" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 256 256"><path d="M167.594 88.393a8.001 8.001 0 0 1 0 11.314l-67.882 67.882a8 8 0 1 1-11.314-11.315l67.882-67.881a8.003 8.003 0 0 1 11.314 0zm-28.287 84.86l-28.284 28.284a40 40 0 0 1-56.567-56.567l28.284-28.284a8 8 0 0 0-11.315-11.315l-28.284 28.284a56 56 0 0 0 79.196 79.197l28.285-28.285a8 8 0 1 0-11.315-11.314zM212.852 43.14a56.002 56.002 0 0 0-79.196 0l-28.284 28.284a8 8 0 1 0 11.314 11.314l28.284-28.284a40 40 0 0 1 56.568 56.567l-28.285 28.285a8 8 0 0 0 11.315 11.314l28.284-28.284a56.065 56.065 0 0 0 0-79.196z" fill="currentColor"></path></svg></span></a> <span>Value-based methods</span></h2> <p data-svelte-h="svelte-v48g1w">In value-based methods, instead of learning a policy function, we <strong>learn a value function</strong> that maps a state to the expected value <strong>of being at that state.</strong></p> <p data-svelte-h="svelte-1wvuk6o">The value of a state is the <strong>expected discounted return</strong> the agent can get if it <strong>starts in that state, and then acts according to our policy.</strong></p> <p data-svelte-h="svelte-1xwf190">“Act according to our policy” just means that our policy is <strong>“going to the state with the highest value”.</strong></p> <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit1/value_1.jpg" alt="Value based RL" width="100%"> <p data-svelte-h="svelte-19buk39">Here we see that our value function <strong>defined values for each possible state.</strong></p> <figure data-svelte-h="svelte-hm65hv"><img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit1/value_2.jpg" alt="Value based RL"> <figcaption>Thanks to our value function, at each step our policy will select the state with the biggest value defined by the value function: -7, then -6, then -5 (and so on) to attain the goal.</figcaption></figure> <p data-svelte-h="svelte-4bnt7i">Thanks to our value function, at each step our policy will select the state with the biggest value defined by the value function: -7, then -6, then -5 (and so on) to attain the goal.</p> <p data-svelte-h="svelte-1uwte4">If we recap:</p> <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit1/vbm_1.jpg" alt="Vbm recap" width="100%"> <img src="https://huggingface.co/datasets/huggingface-deep-rl-course/course-images/resolve/main/en/unit1/vbm_2.jpg" alt="Vbm recap" width="100%"> <a class="!text-gray-400 !no-underline text-sm flex items-center not-prose mt-4" href="https://github.com/huggingface/deep-rl-class/blob/main/units/en/unit1/two-methods.mdx" target="_blank"><svg class="mr-1" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" fill="currentColor" focusable="false" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 32 32"><path d="M31,16l-7,7l-1.41-1.41L28.17,16l-5.58-5.59L24,9l7,7z"></path><path d="M1,16l7-7l1.41,1.41L3.83,16l5.58,5.59L8,23l-7-7z"></path><path d="M12.419,25.484L17.639,6.552l1.932,0.518L14.351,26.002z"></path></svg> <span data-svelte-h="svelte-zjs2n5"><span class="underline">Update</span> on GitHub</span></a>  <p></p> 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