Translations:Diffusion Models Are Real-Time Game Engines/18/en

Given an input interactive environment Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{E}} , and an initial state Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle s_{0} \in \mathcal{S}} , an Interactive World Simulation is a simulation distribution function Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q \left( o_{n} \,|\, \{o_{< n}, a_{\leq n}\} \right), \; o_{i} \in \mathcal{O}, \; a_{i} \in \mathcal{A}} . Given a distance metric between observations $D:{\mathcal {O}}\times {\mathcal {O}}\rightarrow \mathbb {R}$, a policy, i.e., a distribution on agent actions given past actions and observations $\pi \left(a_{n}\,|\,o_{<n},a_{<n}\right)$, a distribution $S_{0}$ on initial states, and a distribution Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N_{0}} on episode lengths, the Interactive World Simulation objective consists of minimizing Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E \left( D \left( o_{q}^{i}, o_{p}^{i} \right) \right)} where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n \sim N_{0}} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 \leq i \leq n} , and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle o_{q}^{i} \sim q, \; o_{p}^{i} \sim V(p)} are sampled observations from the environment and the simulation when enacting the agent’s policy Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \pi} . Importantly, the conditioning actions for these samples are always obtained by the agent interacting with the environment Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{E}} , while the conditioning observations can either be obtained from Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{E}} (the teacher forcing objective) or from the simulation (the auto-regressive objective).