On Mean Field Games for Agents With Langevin Dynamics

Bakshi, Kaivalya; Grover, Piyush; Theodorou, Evangelos A.

doi:10.1109/tcns.2019.2896975

Cited by 11 publications

(18 citation statements)

References 22 publications

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“…The Bellman principle says that the HJB equation is the necessary and sufficient condition for the value function [7]- [9]. Hence, the relative 2-D SPDE is completed by the FPK equation as…”

Section: A Smfg: Hjb and Fpkmentioning

confidence: 99%

“…The main feature of MFGs is the amount of the density of the aforementioned dynamics which is the evolution of the whole population. To this end, the time evolution of probability mass functions (PMFs) is taken into account [7], [8]. This is because the stochastic convolution integrals are required.…”

Section: Introductionmentioning

confidence: 99%

“…McCormack or Lax-Friedrichs methods. In [7], the stability of multi-dimensional non-linear Langevin dynamics and the perturbation ones were theoretically examined. A linear-quadratic MFG for jump-diffusion paradigms was introduced handling the correlation among the agents in [8].…”

Section: Introductionmentioning

confidence: 99%

“…The causal and non-casual knowledge of future data-arrivals about the fractals entail offline (or deterministic) and online (or stochastic) algorithms. 4 Regarding the literature which was discussed above, more acceptable versions of: security-optimality [4]- [7], and stability-tractability [7]- [10], [20], [21] are still required. These open trends motivate us to propose a new scheme relating to which our contribution is as follows.…”

Section: Introductionmentioning

confidence: 99%

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A Novel & Stable Stochastic-Mean-Field-Game for Lossy Source-Coding Paradigms: A Many-Body-Theoretic Perspective

Zamanipour

2019

IEEE Access

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Adaptive controllers and signal processors play a key role in dealing with parameter uncertainties. This paper proposes an adaptive and new information theoretic algorithm for secure and optimal source-coding. We optimise the volume of the achievable rate-distortion-equivocation region by the private Helen's rate (HR), defining a stochastic mean-field game (MFG). The aforementioned stochasticity deals with the additional uncoded side-information (SI) at the encoder-decoder, or even possibly-decoded SI at the eavesdropper (Eve). The stochastic partial derivative equations (SPDEs), namely the Hamilton-Jacobi-Bellman (HJB) and the Fokker-Planck-Kolmogorov (FPK) are presented, being solved by a discretised Lagrangian. We explore the Information-flow over the resultant Riemann-Sphere and our proposed SMFG's stability from a many-body-theoretic perspective. We also show that while the equivocation (uncertainty) rate is ≤ min{H(X), R h }, I(Y; Z|W) which is upper-bounded to min{I(X ; Y), I(Y; Z|W)}, versus I(X ; Z|W) theoretically converges to the information-Bottleneck-bound H(X). Simulation results also show an out-performance of our scheme over the existing work, proving the SMFG's stability and an adequate distance to Pareto-Optimal sets. Our generic solution covers a comprehensive field of studies determining smooth non-linearity.

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Section: A Smfg: Hjb and Fpkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Novel & Stable Stochastic-Mean-Field-Game for Lossy Source-Coding Paradigms: A Many-Body-Theoretic Perspective

Zamanipour

2019

IEEE Access

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show abstract

“…Also, in [13], the dynamics are modeled as weakly nonlinear differential equations which have a linear part for capturing the baseline behavior together with more complicated coupling dynamics for considering more complex phenomena. An interesting class of nonlinear dynamics are gradientflows defined as the negative of gradient of a potential energy function with classical examples of electric and gravitational forces and Langevin dynamics [14]. This type of dynamics appears in modeling physical systems like robots.…”

Section: Introductionmentioning

confidence: 99%