{"url":"/method/v-trace","slug":"v-trace","name":"V-trace","full_name":"V-trace","full_name_withheld":false,"description_markdown":"**V-trace** is an off-policy actor-critic reinforcement learning algorithm that helps tackle the lag between when actions are generated by the actors and when the learner estimates the gradient. Consider a trajectory $\\left(x\\_{t}, a\\_{t}, r\\_{t}\\right)^{t=s+n}\\_{t=s}$ generated by the actor following some policy $\\mu$. We can define the $n$-steps V-trace target for $V\\left(x\\_{s}\\right)$, our value approximation at state $x\\_{s}$ as:\r\n\r\n$$ v\\_{s} = V\\left(x\\_{s}\\right) + \\sum^{s+n-1}\\_{t=s}\\gamma^{t-s}\\left(\\prod^{t-1}\\_{i=s}c\\_{i}\\right)\\delta\\_{t}V $$\r\n\r\nWhere $\\delta\\_{t}V = \\rho\\_{t}\\left(r\\_{t} + \\gamma{V}\\left(x\\_{t+1}\\right) - V\\left(x\\_{t}\\right)\\right)$ is a temporal difference algorithm for $V$, and $\\rho\\_{t} = \\text{min}\\left(\\bar{\\rho}, \\frac{\\pi\\left(a\\_{t}\\mid{x\\_{t}}\\right)}{\\mu\\left(a\\_{t}\\mid{x\\_{t}}\\right)}\\right)$ and $c\\_{i} = \\text{min}\\left(\\bar{c}, \\frac{\\pi\\left(a\\_{t}\\mid{x\\_{t}}\\right)}{\\mu\\left(a\\_{t}\\mid{x\\_{t}}\\right)}\\right)$ are truncated importance sampling weights. 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