Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stronger Calibration Lower Bounds via Sidestepping   We consider an online binary prediction setting where a forecaster observes a
sequence of $T$ bits one by one. Before each bit is revealed, the forecaster
predicts the probability that the bit is $1$. The forecaster is called
well-calibrated if for each $p \in [0, 1]$, among the $n_p$ bits for which the
forecaster predicts probability $p$, the actual number of ones, $m_p$, is
indeed equal to $p \cdot n_p$. The calibration error, defined as $\sum_p |m_p -
p n_p|$, quantifies the extent to which the forecaster deviates from being
well-calibrated. It has long been known that an $O(T^{2/3})$ calibration error
is achievable even when the bits are chosen adversarially, and possibly based
on the previous predictions. However, little is known on the lower bound side,
except an $\Omega(\sqrt{T})$ bound that follows from the trivial example of
independent fair coin flips.
  In this paper, we prove an $\Omega(T^{0.528})$ bound on the calibration
error, which is the first super-$\sqrt{T}$ lower bound for this setting to the
best of our knowledge. The technical contributions of our work include two
lower bound techniques, early stopping and sidestepping, which circumvent the
obstacles that have previously hindered strong calibration lower bounds. We
also propose an abstraction of the prediction setting, termed the
Sign-Preservation game, which may be of independent interest. This game has a
much smaller state space than the full prediction setting and allows simpler
analyses. The $\Omega(T^{0.528})$ lower bound follows from a general reduction
theorem that translates lower bounds on the game value of Sign-Preservation
into lower bounds on the calibration error.

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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: econ