  This article recalls the recent work on a linear programming formulation of
infinite horizon risk-sensitive control via its equivalence with a single
controller game, using a classic work of Vrieze. This is then applied to a
constrained risk-sensitive control problem with a risk-sensitive cost and
risk-sensitive constraint. This facilitates a Lagrange multiplier based
resolution thereof. In the process, this leads to an unconstrained linear
program and its dual, parametrized by a parameter that is a surrogate for
Lagrange multiplier. This also opens up the possibility of a primal - dual type
numerical scheme wherein the linear program is a subroutine within the
subgradient ascent based update rule for the Lagrange multiplier. This
equivalent unconstrained risk-sensitive control formulation does not seem
obvious without the linear programming equivalents as intermediaries. We also
discuss briefly other related algorithmic possibilities for future research.
