We methodologically address the problem of Qvalue overestimation in deep reinforcement learning to handle high-dimensional state spaces efficiently. By adapting concepts from information theory, we introduce an intrinsic penalty signal encouraging reduced Q-value estimates. The resultant algorithm encompasses a wide range of learning outcomes containing deep Q-networks as a special case. Differ...

The Lagrange multiplier for the kinetic energy e is shown to be −γcm on a singular arc, where γ (g/J) is derived from engine and driveline characteristics and cm ≈ 1. Using this value as an approximation for constrained arcs as well, the cost function is J(s, x) ≈ −γcme + C(s) that yields the residual cost φ(x) = −γcme. The factor β corresponds to the constant Lagrange multiplier for time and i...

This document gives the formal proofs of the following results about the sums of two and four squares: 1. Any prime number p ≡ 1 mod 4 can be written as the sum of two squares. 2. (Lagrange) Any natural number can be written as the sum of four

We prove Rubio de Francia’s Littlewood-Paley inequality for arbitrary disjoint intervals in the noncommutative setting, i.e. for functions with values in noncommutative L-spaces. As applications, we get sufficient conditions in terms of q-variation for the boundedness of Schur multipliers on Schatten classes.

The paper deals with a general optimal control problem for age-structured systems. A necessary optimality condition of Pontryagin type is obtained, where the novelty is in that mixed control-state constraints are present. The proof uses an abstract Lagrange multiplier theorem, and the main difficulty is to obtain regularity of the Lagrange multipliers in the particular problem at hand.

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We present a new architecture for signed multiplication which maintains the pure form of an array multiplier, exhibiting a much lower overhead than the Booth architecture. This architecture is extended for radixencoding, which leads to a reduction of the number of partial lines, enabling a significant improvement in performance and power consumption. The flexibility of our architecture allows f...

1. Introduction. The Lagrange inversion formula is one of the fundamental results of enumerative combinatorics. It expresses the coefficients of powers of the compositional inverse of a power series in terms of the coefficients of powers of the original power series. G. Labelle [10] extended Lagrange inversion to cycle index series, which are equivalent to symmetric functions. Although motivate...

We study homological invariants of smooth families of real quadratic forms as a step towards a “ Lagrange multipliers rule in the large” that intends to describe topology of smooth vector functions in terms of scalar Lagrange functions.