Let $D$ be a distribution over bitstring/label pairs $\{0,1\}^d\times \{0,1\}$ and let $C$ be a collection of boolean valued functions $f:\{0,1\}^d\rightarrow\{0,1\}$. For each function $f \in C$, let: $$err(f,D) = \Pr_{(x,y) \sim D}[f(x) \neq y]$$ and let: $$OPT(C,D) = \min_{f \in C}\ err(f,D)$$ Say that an algorithm $A$ agnostically learns $C$ over any distribution, if for any $D$ it can with probability $2/3$ find a function $f$ such that $err(f,D) \leq OPT(C,D) + \epsilon$, given time and a number of samples from $D$ that is bounded by a polynomial in $d$ and $1/\epsilon$.
Question: What classes of functions $C$ are known to be agnostically learnable over arbitrary distributions?
No class is too simple! I know that even monotone conjunctions are not known to be agnostically learnable over arbitrary distributions, so I'm just looking for nontrivial classes of functions.