162,654 research outputs found
Learning Robust Deep Equilibrium Models
Deep equilibrium (DEQ) models have emerged as a promising class of implicit
layer models in deep learning, which abandon traditional depth by solving for
the fixed points of a single nonlinear layer. Despite their success, the
stability of the fixed points for these models remains poorly understood.
Recently, Lyapunov theory has been applied to Neural ODEs, another type of
implicit layer model, to confer adversarial robustness. By considering DEQ
models as nonlinear dynamic systems, we propose a robust DEQ model named LyaDEQ
with guaranteed provable stability via Lyapunov theory. The crux of our method
is ensuring the fixed points of the DEQ models are Lyapunov stable, which
enables the LyaDEQ models to resist minor initial perturbations. To avoid poor
adversarial defense due to Lyapunov-stable fixed points being located near each
other, we add an orthogonal fully connected layer after the Lyapunov stability
module to separate different fixed points. We evaluate LyaDEQ models on several
widely used datasets under well-known adversarial attacks, and experimental
results demonstrate significant improvement in robustness. Furthermore, we show
that the LyaDEQ model can be combined with other defense methods, such as
adversarial training, to achieve even better adversarial robustness
Robust learning stability with operational monetary policy rules
We consider the robust stability of a rational expectations equilibrium, which we define as stability under discounted (constant gain) least-squares learning, for a range of gain parameters. We find that for operational forms of policy rules, ie rules that do not depend on contemporaneous values of endogenous aggregate variables, many interest-rate rules do not exhibit robust stability. We consider a variety of interest-rate rules, including instrument rules, optimal reaction functions under discretion or commitment, and rules that approximate optimal policy under commitment. For some reaction functions we allow for an interest-rate stabilization motive in the policy objective. The expectations-based rules proposed in Evans and Honkapohja (2003, 2006) deliver robust learning stability. In contrast, many proposed alternatives become unstable under learning even at small values of the gain parameter.commitment; interest-rate setting; adaptive learning; stability; determinacy
Robust Learning Stability with Operational Monetary Policy Rules
We consider “robust stability” of a rational expectations equilibrium, which we define as stability under discounted (constant gain) least-squares learning, for a range of gain parameters. We find that for operational forms of policy rules, i.e. rules that do not depend on contemporaneous values of endogenous aggregate variables, many interest-rate rules do not exhibit robust stability. We consider a variety of interest-rate rules, including instrument rules, optimal reaction functions under discretion or commitment, and rules that approximate optimal policy under commitment. For some reaction functions we allow for an interest-rate stabilization motive in the policy objective. The expectations-based rules proposed in Evans and Honkapohja (2003, 2006) deliver robust learning stability. In contrast, many proposed alternatives become unstable under learning even at small values of the gain parameter.Commitment, interest-rate setting, adaptive learning, stability, determinacy.
Robust Learning Stability with Operational Monetary Policy Rules
We consider robust stability under learning of alternative interest-rate rules. By “robust stability” we mean stability of the rational expectations equilibrium, under discounted (constant gain) least-squares learning, for a range of gain parameters. We find that many interest-rate rules are not robust, in this sense, when operational forms of policy rules are employed. Rules are considered operational if they do not depend on contemporaneous values of endogenous aggregate variables. We consider a variety of interest-rate rules, including instrument rules, optimal reaction functions under discretion or commitment, and rules that approximate optimal policy under commitment. For some of the rules that aim to achieve optimal policy, we allow for an interest-rate stabilization motive in the policy objective. The expectations-based rules proposed in Evans and Honkapohja (2003, 2006) deliver robust learning stability. In contrast, many proposed alternatives become unstable under learning even at small values of the gain parameter.
Probably Approximately Correct Nash Equilibrium Learning
We consider a multi-agent noncooperative game with agents' objective
functions being affected by uncertainty. Following a data driven paradigm, we
represent uncertainty by means of scenarios and seek a robust Nash equilibrium
solution. We treat the Nash equilibrium computation problem within the realm of
probably approximately correct (PAC) learning. Building upon recent
developments in scenario-based optimization, we accompany the computed Nash
equilibrium with a priori and a posteriori probabilistic robustness
certificates, providing confidence that the computed equilibrium remains
unaffected (in probabilistic terms) when a new uncertainty realization is
encountered. For a wide class of games, we also show that the computation of
the so called compression set - a key concept in scenario-based optimization -
can be directly obtained as a byproduct of the proposed solution methodology.
Finally, we illustrate how to overcome differentiability issues, arising due to
the introduction of scenarios, and compute a Nash equilibrium solution in a
decentralized manner. We demonstrate the efficacy of the proposed approach on
an electric vehicle charging control problem.Comment: Preprint submitted to IEEE Transactions on Automatic Contro
Learning Dynamics in Monetary Policy: The Robustness of an Aggressive Price Stabilizing Policy
This paper investigates the effect of an aggressive inflation stabilizing monetary policy on the ability of agents to reach a rational expectations equilibrium for inflation and output. Using an adaptive learning framework, we develop a model that combines a real wage contracting rigidity with an interest rate rule. We show that an AR(1) equilibrium requires more aggressive monetary policy to achieve both determinacy and learnability. This model and policy findings contrast with Bullard and Mitra’s [Determinacy, learnability and monetary policy inertia (2001); Journal of Monetary Economics 49 (2002) 1105] model (no inflation persistence) and policy findings (less aggressive policy). These results suggest that aggressive policy is robust in different model specifications
Learning Dynamics in Monetary Policy: The Robustness of an Aggressive Price Stabilizing Policy
This paper investigates the effect of an aggressive inflation stabilizing monetary policy on the ability of agents to reach a rational expectations equilibrium for inflation and output. Using an adaptive learning framework, we develop a model that combines a real wage contracting rigidity with an interest rate rule. We show that an AR(1) equilibrium requires more aggressive monetary policy to achieve both determinacy and learnability. This model and policy findings contrast with Bullard and Mitra’s [Determinacy, learnability and monetary policy inertia (2001); Journal of Monetary Economics 49 (2002) 1105] model (no inflation persistence) and policy findings (less aggressive policy). These results suggest that aggressive policy is robust in different model specifications
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