TODO: 结合RL原理、图示、代码,对PPO计算流程加以说明

ϕ=arg max⁡ϕEs∼p(s;ϕ)12min⁡(∣∣rt+γVπ(st+1)−V~π(st)∣∣22‾,∣∣rt+γVπ(st+1)−clip(V~π(st),Vminπ,Vmaxπ)∣∣22‾)\phi = \argmax_{\phi} E_{s \sim p(s;\phi)} \frac{1}{2} \min \left( \underline{ || r_t + \gamma V^{\pi}(s_{t+1}) - \tilde{V}^{\pi}(s_t) ||_2^2 }, \underline{ || r_t + \gamma V^{\pi}(s_{t+1}) - \text{clip}( \tilde{V}^{\pi}(s_t), V^{\pi}_{min}, V^{\pi}_{max} ) ||_2^2 } \right)

θ~=arg max⁡θ~Es∼p(s;θ),a∼π(a∣s;θ)min⁡(π(a∣s;θ~)π(a∣s;θ)A(s,a;θ)‾,clip(π(a∣s;θ~)π(a∣s;θ),1−ϵ,1+ϵ)A(s,a;θ)‾)\tilde{\theta} = \argmax_{\tilde{\theta}} E_{s \sim p(s;\theta), a \sim \pi(a|s;\theta)} \min \left( \underline{ \frac{\pi(a|s;\tilde{\theta})}{\pi(a|s; \theta)} A(s, a; \theta) }, \underline{ \text{clip} ( \frac{\pi(a|s;\tilde{\theta})}{\pi(a|s; \theta)}, 1 - \epsilon, 1 + \epsilon ) A(s, a; \theta) } \right)