Fig. 1. Schematic of reinforcement learning

Fig. 2. Optoelectronic RL using semiconductor lasers to generate random numbers. (a) Ultrafast RL based on laser chaos^[29]; (b) scalable RL by time-division multiplexing of laser chaos^[33]; (c) RL based on dual-channel laser chaos^[36]; (d) RL based on triple-channel laser chaos^[37]

Fig. 3. Optoelectronic RL by controlling the physical dynamics in the laser cavity. (a) RL based on mode switching in a ring laser^[42]; (b) RL based on lag synchronization of laser chaos^[34]; (c) RL based on a laser network in a ring configuration^[38]; (d) RL based on chaotic itinerancy in a multimode semiconductor laser^[41]

Fig. 4. Classical reservoir computing. (a) Schematic illustration of classical reservoir computing; (b) reservoir computing based on a large-area vertical cavity surface emitting laser (LA-VCSEL)^[45]

Fig. 5. Principle of delay-based reservoir computing^[47]. (a) Schematic illustration of delay-based reservoir computing; (b) scheme of input data preparation

Fig. 6. Optoelectronic RC using lasers with optical delayed feedback. (a) RC based on a semiconductor laser^[51]; (b) RC based on a semiconductor ring laser^[52]; (c) RC based on a microchip laser^[53]; (d) RC based on a VCSEL^[54]; (e) four-channel RC based on two mutually coupled VCSELs^[56]; (f) dual-training scheme of RC based on a single VCSEL^[57]

Fig. 7. RC based on photonic integrated circuits (PIC) and parallel and deep RC. (a) RC using single semiconductor laser on a PIC^[63]; (b) RC using multiple semiconductor lasers in parallel on a PIC^[64]; (c) configurations of single reservoir, parallel reservoirs, deep reservoirs, and hybrid reservoirs^[65]

Fig. 8. Photonic Ising machine based on injection-locked laser network. (a) Schematic illustration of an injection-locked laser network^{[20, 69]}; (b) 2-spin Ising machine based on semiconductor lasers^[70]; (c)(d) photonic Ising machine based on multi-core fiber lasers^[71-72]

Fig. 9. Photonic Ising machine based on degenerate optical parametric oscillator network. (a) 4-spin photonic Ising machine^[22]; (b) 100-spin photonic Ising machine^[73]; (c) 2000-spin photonic Ising machine^[74]; (d) 100000-spin photonic Ising machine^[76]

Fig. 10. Configuration of degenerate cavity laser^[81]

Fig. 11. XY model simulator based on degenerate cavity laser. (a) Steady state of the laser network in the degenerate cavity laser (DCL) is mapped to the ground state of an XY model^[87]; (b) rapid analysis of the ground-state degeneracy of an XY model using DCL^[89]; (c) improving the sensitivity to loss differences by inserting a saturable absorber at the far field (FF) plane^[90]; (d) obtaining exact mapping to XY model by equalizing the amplitudes of laser channels^[91]

Fig. 12. Solving other computational problems based on DCL. (a) High-speed wavefront shaping using a DCL^[92]; (b) rapidly solving the phase retrieval problem using a digital degenerate cavity laser (DDCL)^[93]; (c) generation of high-resolution arbitrary-shaped laser beams using a DDCL^[94]; (d) high-speed full-field imaging through scattering media using a DCL^[95]